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