A Global Bayesian Analysis of Neutrino Mass Data

TL;DR

This paper presents the first global Bayesian analysis of neutrino masses by coherently combining oscillation data, precision cosmology, and neutrinoless double beta decay results within a three-neutrino Majorana framework. The authors construct an eight-parameter model, compare two priors on the lightest neutrino mass, and evaluate the joint posterior distributions for observables like the effective Majorana mass $|m_{ee}|$ and the sum of masses $\Sigma$, as well as the discovery potential for $0νββ$ experiments. They find a mild preference for normal ordering that is robust to prior choices and cosmological datasets, and show that $0νββ$ discovery prospects vary widely with mass ordering, exposure, and background levels. The methodology provides a transparent, updateable approach for integrating forthcoming data and improving inference on the absolute neutrino mass scale and Majorana nature.

Abstract

We perform a global Bayesian analysis of currently available neutrino data, putting data from oscillation experiments, neutrinoless double beta decay ($0νββ$), and precision cosmology on an equal footing. We evaluate the discovery potential of future $0νββ$ experiments and the Bayes factor of the two possible neutrino mass ordering schemes for different prior choices. We show that the indication for normal ordering is still very mild and does not strongly depend on realistic prior assumptions or different combinations of cosmological data sets. We find a wide range for $0νββ$ discovery potential, depending on the absolute neutrino mass scale, mass ordering and achievable background level.

Figures (10)

• Figure 1: Heat map of posterior probability density for both combinations of cosmological data sets and choices of the prior on $m_{\mathrm{lightest}}$. The upper panels depict the flat prior while the lower panels show the log prior. See text for definitions of the different quantities.
• Figure 2: Cumulative distribution function for $T_{1/2}$ for both ${}^{76}$Ge and ${}^{136}$Xe (conservative cosmology). The distributions on the left feature a prior flat in $m_{\mathrm{lightest}}$, while the ones on the right feature a prior flat in $\log(m_{\mathrm{lightest}}$).
• Figure 3: Discovery potential as a function of effective exposure $E \epsilon$ for different background levels. The upper left panel defines a benchmark case (germanium, IO, conservative cosmology), while for the other panels one of these parameters is changed: upper right -- NO; lower left -- restrictive cosmology; lower right -- ${}^{136}$Xe. The kinks in the curves are a consequence of the integer nature of Poissonian statistics.
• Figure 4: Posterior probability distributions of the NMEs, sorted into 500 bins, for both ${}^{76}$Ge and ${}^{136}$Xe, along with the input values. As can be seen, the posterior probabilities basically reproduce the input, i.e., the current constraints are not sufficiently strong to impact NME computations.
• Figure 5: Likelihood functions for the squared mass differences (left) and for the relevant mixing angles (right).