Bayesian global analysis of neutrino oscillation data

TL;DR

This work presents a comprehensive Bayesian global analysis of three-flavor neutrino oscillation data, contrasting posterior inferences with standard χ^2 results and properly accounting for the circular nature of the CP phase $\delta_{CP}$. Using Haar-measure priors on the mixing matrix and marginalization over nuisance parameters, the authors show that key parameters $\Delta m^2_{3\ell}$, $\Delta m^2_{21}$, $\sin^2\theta_{12}$, and $\sin^2\theta_{13}$ are well constrained with near-Gaussian posteriors, while mass ordering, $\theta_{23}$ octant, and CP violation show only weak Bayesian evidence. The analysis reveals order-dependent shifts in $\delta_{CP}$ and $s^2_{23}$, a modest preference for the second octant in certain orderings, and nontrivial correlations between $s^2_{23}$ and $\delta_{CP}$, quantified through several circular and information-theoretic measures. Overall, Bayesian results corroborate many χ^2 conclusions but provide a principled framework for model comparison and for describing complex dependencies in the data without overinterpreting weak signals such as CP violation.

Abstract

We perform a Bayesian analysis of current neutrino oscillation data. When estimating the oscillation parameters we find that the results generally agree with those of the $χ^2$ method, with some differences involving $s_{23}^2$ and CP-violating effects. We discuss the additional subtleties caused by the circular nature of the CP-violating phase, and how it is possible to obtain correlation coefficients with $s_{23}^2$. When performing model comparison, we find that there is no significant evidence for any mass ordering, any octant of $s_{23}^2$ or a deviation from maximal mixing, nor the presence of CP-violation.

Figures (7)

• Figure 1: One-dimensional posterior distributions (black full lines) and two-dimensional $1\sigma$, $2\sigma$ and $3\sigma$ Bayesian credible regions (black void contours). The figure also shows the one-dimensional profile likelihoods (red dashed curves) and two-dimensional $\chi^2$ regions (coloured filled regions) from Ref. Gonzalez-Garcia:2014bfa.
• Figure 2: Same as Fig. \ref{['fig:param_NO']} but for IO.
• Figure 3: Same as Fig. \ref{['fig:param_NO']} but for MO.
• Figure 4: Bayesian posterior/marginal likelihood (black solid), plotted together with the profile likelihood (black dashed), from Ref. Gonzalez-Garcia:2014bfa (both normalized to their maximal value). The number number of $\sigma's$)(red solid), and $\sqrt{\Delta \chi^2}$ (red dashed). Posterior mean (yellow line), median (green), and maximum of the marginal likelihood (cyan). NO (top left), IO (top right), MO (bottom).
• Figure 5: Left plots: same as Fig. \ref{['fig:snq23_comb']} for $\delta_{\rm CP}$. Right plots: Same as left plots, but with only posterior and profile likelihood and plotted in polar coordinates. For clarity, half of the maximal radius corresponds to zero function value.