# Strong Bayesian Evidence for the Normal Neutrino Hierarchy

## TL;DR

This paper uses Bayesian analysis of cosmological and neutrino oscillation data to strongly favor the normal neutrino mass hierarchy with odds of 42:1, and infers individual neutrino masses.

## Contribution

It provides the first strong Bayesian evidence favoring the normal neutrino hierarchy by combining cosmological and oscillation data with a minimally informative prior.

## Key findings

- Odds of 42:1 in favor of the normal hierarchy
- Inferred neutrino masses with credible intervals
- Discussion on future data impact on hierarchy odds

## Abstract

The configuration of the three neutrino masses can take two forms, known as the normal and inverted hierarchies. We compute the Bayesian evidence associated with these two hierarchies. Previous studies found a mild preference for the normal hierarchy, and this was driven by the asymmetric manner in which cosmological data has confined the available parameter space. Here we identify the presence of a second asymmetry, which is imposed by data from neutrino oscillations. By combining constraints on the squared-mass splittings with the limit on the sum of neutrino masses of $\Sigma m_\nu < 0.13$ eV, and using a minimally informative prior on the masses, we infer odds of 42:1 in favour of the normal hierarchy, which is classified as "strong" in the Jeffreys' scale. We explore how these odds may evolve in light of higher precision cosmological data, and discuss the implications of this finding with regards to the nature of neutrinos. Finally the individual masses are inferred to be $m_1 = 3.80^{+26.2}_{-3.73} \, \text{meV}, m_2 = 8.8^{+18}_{-1.2} \, \text{meV}, m_3 = 50.4^{+5.8}_{-1.2} \, \text{meV}$ ($95\%$ credible intervals).