Bayesian constraints on θ13 from 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)theta(12), sin(2)theta(13): (1) a traditional flat uninformative prior; and (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(21)(2) 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 [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)theta(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).].