Constraints on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>θ</mml:mi><mml:mn>13</mml:mn></mml:msub></mml:math>from a three-flavor oscillation analysis of reactor antineutrinos at KamLAND

We present new constraints on the neutrino oscillation parameters $\ensuremath{\Delta}{m}_{21}^{2}$, ${\ensuremath{\theta}}_{12}$, and ${\ensuremath{\theta}}_{13}$ from a three-flavor analysis of solar and KamLAND data. The KamLAND data set includes data acquired following a radiopurity upgrade and amounts to a total exposure of $3.49\ifmmode\times\else\texttimes\fi{}{10}^{32}$ target-proton-year. Under the assumption of $CPT$ invariance, a two-flavor analysis (${\ensuremath{\theta}}_{13}=0$) of the KamLAND and solar data yields the best-fit values ${tan}^{2}{\ensuremath{\theta}}_{12}={0.444}_{\ensuremath{-}0.030}^{+0.036}$ and $\ensuremath{\Delta}{m}_{21}^{2}={7.50}_{\ensuremath{-}0.20}^{+0.19}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }\text{ }{\mathrm{eV}}^{2}$; a three-flavor analysis with ${\ensuremath{\theta}}_{13}$ as a free parameter yields the best-fit values ${tan}^{2}{\ensuremath{\theta}}_{12}={0.452}_{\ensuremath{-}0.033}^{+0.035}$, $\ensuremath{\Delta}{m}_{21}^{2}={7.50}_{\ensuremath{-}0.20}^{+0.19}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }\text{ }{\mathrm{eV}}^{2}$, and ${sin}^{2}{\ensuremath{\theta}}_{13}={0.020}_{\ensuremath{-}0.016}^{+0.016}$. This ${\ensuremath{\theta}}_{13}$ interval is consistent with other recent work combining the CHOOZ, atmospheric and long-baseline accelerator experiments. We also present a new global ${\ensuremath{\theta}}_{13}$ analysis, incorporating the CHOOZ, atmospheric, and accelerator data, which indicates ${sin}^{2}{\ensuremath{\theta}}_{13}={0.009}_{\ensuremath{-}0.007}^{+0.013}$. A nonzero value is suggested, but only at the 79% C.L.