Objective Bayesian analysis of neutrino masses and hierarchy

TL;DR

This paper develops a minimally informative Bayesian prior for neutrino mass analysis, finding the normal hierarchy slightly favored but inconclusive, and emphasizes the need for better data to determine neutrino properties.

Contribution

It introduces an objective Bayesian reference prior for neutrino mass analysis, reducing prior bias and clarifying data requirements for hierarchy determination.

Findings

Normal hierarchy slightly favored with 5.1:1 odds

Future cosmological data can provide conclusive evidence

Inverted hierarchy detection remains challenging with current uncertainties

Abstract

Given the precision of current neutrino data, priors still impact noticeably the constraints on neutrino masses and their hierarchy. To avoid our understanding of neutrinos being driven by prior assumptions, we construct a prior that is mathematically minimally informative. Using the constructed uninformative prior, we find that the normal hierarchy is favoured but with inconclusive posterior odds of 5.1:1. Better data is hence needed before the neutrino masses and their hierarchy can be well constrained. We find that the next decade of cosmological data should provide conclusive evidence if the normal hierarchy with negligible minimum mass is correct, and if the uncertainty in the sum of neutrino masses drops below 0.025 eV. On the other hand, if neutrinos obey the inverted hierarchy, achieving strong evidence will be difficult with the same uncertainties. Our uninformative prior was constructed from principles of the Objective Bayesian approach. The prior is called a reference prior and is minimally informative in the specific sense that the information gain after collection of data is maximised. The prior is computed for the combination of neutrino oscillation data and cosmological data and still applies if the data improve.