Bayesian Constraints on theta_{13} from Solar and KamLAND Neutrino Data

TL;DR

This paper uses Bayesian methods to analyze solar and KamLAND neutrino data, assessing the parameter theta_{13} with different priors, confirming a weak hint of theta_{13} > 0 and examining how additional data affects this indication.

Contribution

It introduces a Bayesian framework with different priors to constrain theta_{13} using solar and KamLAND data, updating the significance of the theta_{13} hint.

Findings

Confirmed a 1.2 sigma hint of theta_{13} > 0 from solar and KamLAND data.

The significance of the theta_{13} hint is reduced to about 0.8 sigma when including atmospheric and long-baseline data.

Different prior choices influence the posterior distribution of theta_{13}.

Abstract

We present the results of a Bayesian analysis of solar and KamLAND neutrino data in the framework of three-neutrino mixing. We adopt two approaches for the prior probability distribution of the oscillation parameters Delta m^2_{21}, sin^2 theta_{12}, sin^2 theta_{13}: 1) a traditional flat uninformative prior; 2) an informative prior which describes the limits on sin^2 theta_{13} obtained in atmospheric and long-baseline accelerator and reactor neutrino experiments. In both approaches, we present the allowed regions in the sin^2 theta_{13} - Delta m^2_{21} and sin^2 theta_{12} - sin^2 theta_{13} planes, as well as the marginal posterior probability distribution of sin^2 theta_{13}. We confirm the 1.2 sigma hint of theta_{13} > 0 found in hep-ph/0806.2649 from the analysis of solar and KamLAND neutrino data. We found that the statistical significance of the hint is reduced to about 0.8 sigma by the constraints on sin^2 theta_{13} coming from atmospheric and long-baseline accelerator and reactor neutrino data, in agreement with arXiv:0808.2016.