Strong Bayesian Evidence for the Normal Neutrino Hierarchy

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 $m_1=3.80_{-3.73}^{+26.2}\text{meV},m_2=8.8_{-1.2}^{+18}\text{meV},m_3=50.4_{-1.2}^{+5.8}\text{meV}$ ($95\%$ credible intervals).

Matches accepted version in JCAP. We provide publicly available priors for forthcoming investigations https://github.com/frgsimpson/neutrino-priors Conclusions with regard to the hierarchy are unchanged: we show that current data robustly prefer the normal hierarchy, by employing the least informative priors, with strong bayesian odds

References in corpus (8)

• Massive neutrinos and cosmology
• Updated fit to three neutrino mixing: status of leptonic CP violation
• Physics Potential of a Long Baseline Neutrino Oscillation Experiment Using J-PARC Neutrino Beam and Hyper-Kamiokande
• Finding Evidence for Massive Neutrinos using 3D Weak Lensing
• The smallest neutrino mass
• A high-resolution CMOS imaging detector for the search of neutrinoless double $\beta$ decay in ${}^{82}$Se
• A neutrino mass-mixing sum rule from SO(10) and neutrinoless double beta decay
• Relativistic Cyclotron Radiation Detection of Tritium Decay Electrons as a New Technique for Measuring the Neutrino Mass

Cited by in corpus (50)

• How to Measure Galaxy Star Formation Histories II: Nonparametric Models
• New physics in light of the $H_0$ tension: an alternative view
• Unveiling $\nu$ secrets with cosmological data: neutrino masses and mass hierarchy
• Tale of stable interacting dark energy, observational signatures, and the $H_0$ tension
• How to measure galaxy star-formation histories I: Parametric models
• Constraints on the sum of the neutrino masses in dynamical dark energy models with $w(z)\ge -1$ are tighter than those obtained in $\Lambda$CDM
• Revisiting a negative cosmological constant from low-redshift data
• Neutrino Mass Ordering from Oscillations and Beyond: 2018 Status and Future Prospects
• Reducing the $H_0$ and ${\sigma }_8$ tensions with Dark Matter-neutrino interactions
• No evidence for extensions to the standard cosmological model
• Updated results on neutrino mass and mass hierarchy from cosmology with Planck 2018 likelihoods
• Discovery probability of next-generation neutrinoless double-$\beta$ decay experiments
• Scale-dependent galaxy bias, CMB lensing-galaxy cross-correlation, and neutrino masses
• Neutrino cosmology after DESI: tightest mass upper limits, preference for the normal ordering, and tension with terrestrial observations
• Constraining Neutrino Masses, the Cosmological Constant and BSM Physics from the Weak Gravity Conjecture
• Bias due to neutrinos must not uncorrect'd go
• Dawn of the dark: unified dark sectors and the EDGES Cosmic Dawn 21-cm signal
• Primordial black holes from single-field inflation: a fine-tuning audit
• Do current cosmological observations rule out all Covariant Galileons?
• A Global Bayesian Analysis of Neutrino Mass Data
• The road ahead of Horndeski: cosmology of surviving scalar-tensor theories
• Constraints on quintessence scalar field models using cosmological observations
• Objective Bayesian analysis of neutrino masses and hierarchy
• Bayesian evidence for the tensor-to-scalar ratio $r$ and neutrino masses $m_{\nu }$: Effects of uniform vs logarithmic priors
• Neutrino Mass Priors for Cosmology from Random Matrices
• Neutrino mass and mass ordering: No conclusive evidence for normal ordering
• Neutrino Masses and Mass Hierarchy: Evidence for the Normal Hierarchy
• DEMNUni: comparing nonlinear power spectra prescriptions in the presence of massive neutrinos and dynamical dark energy
• Cosmology-marginalized approaches in Bayesian model comparison: the neutrino mass as a case study
• Quantifying the tension between cosmological and terrestrial constraints on neutrino masses
• A Bayesian analysis of inflationary primordial spectrum models using Planck data
• Profile Likelihoods in Cosmology: When, Why and How illustrated with $\Lambda$CDM, Massive Neutrinos and Dark Energy
• Revisiting the impact of neutrino mass hierarchies on neutrino mass constraints in light of recent DESI data
• Update constraints on neutrino mass and mass hierarchy in light of dark energy models
• KiDS-1000 Cosmology: machine learning -- accelerated constraints on Interacting Dark Energy with COSMOPOWER
• Probing the Neutrino Mass Hierarchy beyond $\Lambda$CDM Model
• A novel model-marginalized cosmological bound on the QCD axion mass
• Wake forces in a background of quadratically coupled mediators
• Impact of the damping tail on neutrino mass constraints
• Maximum-Entropy Priors with Derived Parameters in a Specified Distribution
• Target Neutrino Mass Precision for Determining the Neutrino Hierarchy
• Impact of Massive Neutrinos and Dark Radiation on the High-redshift Cosmic Web. I. Lyman-Alpha Forest Observables
• Can an unbroken flavour symmetry provide an approximate description of lepton masses and mixing?
• Finding structure in the dark: coupled dark energy, weak lensing, and the mildly nonlinear regime
• The Exposure-Background Duality in the Searches of Neutrinoless Double Beta Decay
• Sound-Horizon-Agnostic Inference of the Hubble Constant and Neutrino Mass from BAO, CMB Lensing, and Galaxy Weak Lensing and Clustering
• String Landscape and Fermion Masses
• Covert symmetries in the neutrino mass matrix
• Cosmological Constraints on Neutrino Masses in a Second-Order CPL Dark Energy Model
• Improved cosmological constraints on the neutrino mass and lifetime