Bayesian constraints onϑ13from solar and KamLAND neutrino data

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 $\Delta m_{21}^2$, ${sin}^2{\vartheta }_{12}$, ${sin}^2{\vartheta }_{13}$: (1) a traditional flat uninformative prior; and (2) an informative prior which describes the limits on ${sin}^2{\vartheta }_{13}$ obtained in atmospheric and long-baseline accelerator and reactor neutrino experiments. In both approaches, we present the allowed regions in the ${sin}^2{\vartheta }_{13}\mathrm{\text{−}}\Delta m_{21}^2$ and ${sin}^2{\vartheta }_{12}\mathrm{\text{−}}{sin}^2{\vartheta }_{13}$ planes, as well as the marginal posterior probability distribution of ${sin}^2{\vartheta }_{13}$. We confirm the $1.2\sigma$ hint of ${\vartheta }_{13}>0$ found in [G. Fogli et al., Phys. Rev. Lett. 101, 141801 (2008).] 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 ${sin}^2{\vartheta }_{13}$ coming from atmospheric and long-baseline accelerator and reactor neutrino data, in agreement with [T. Schwetz, M. Tortola, and J. W. F. Valle, New J. Phys. 10, 113011 (2008).].