Neutrino mass and mass ordering: No conclusive evidence for normal ordering

TL;DR

This paper critically examines claims of strong Bayesian evidence favoring the normal neutrino mass ordering, finding no conclusive support and emphasizing the importance of priors and parameterizations in such analyses.

Contribution

It demonstrates that current evidence for normal neutrino mass ordering is not robust and depends heavily on priors and parameterizations used in the analysis.

Findings

No decisive Bayesian evidence for normal ordering was found.

The significance of favoring normal ordering is about 2.7 sigma, mainly from oscillation data.

Results vary significantly with different priors and parameterizations.

Abstract

The extraction of the neutrino mass ordering is one of the major challenges in particle physics and cosmology, not only for its implications for a fundamental theory of mass generation in nature, but also for its decisive role in the scale of future neutrinoless double beta decay experimental searches. It has been recently claimed that current oscillation, beta decay and cosmological limits on the different observables describing the neutrino mass parameter space provide robust decisive Bayesian evidence in favor of the normal ordering of the neutrino mass spectrum [arXiv:2203.14247]. We further investigate these strong claims using a rich and wide phenomenology, with different sampling techniques of the neutrino parameter space. Contrary to the findings of Jimenez et al [arXiv:2203.14247], no decisive evidence for the normal mass ordering is found. Neutrino mass ordering analyses must rely on priors and parameterizations that are ordering-agnostic: robust results should be regarded as those in which the preference for the normal neutrino mass ordering is driven exclusively by the data, while we find a difference of up to a factor of 33 in the Bayes factors among the different priors and parameterizations exploited here. An ordering-agnostic prior would be represented by the case of parameterizations sampling over the two mass splittings and a mass scale, or those sampling over the individual neutrino masses via normal prior distributions only. In this regard, we show that the current significance in favor of the normal mass ordering should be taken as $2.7\sigma$ (i.e. moderate evidence), mostly driven by neutrino oscillation data.