Global Analysis of Solar Neutrino and KamLAND Data

A global analysis of the data from all the solar neutrino experiments combined with the recent KamLAND data is presented. A formula frequently used in the literature gives survival probability for three active solar neutrino flavors in terms of a suitably-modified two-flavor survival probability. Corrections to this formula, which depend on $\theta_{13}$ and $\delta m_{31}^2$, are calculated. For the mass scale suggested by the atmospheric neutrino experiments the contributions of $\delta m_{31}^2$ to these corrections is found to be negligible. The role of $\theta_{13}$ in solar neutrino physics is elaborated. For electron neutrino oscillations into another active flavor, we find best fit values of $\tan^2 \theta_{12} \sim 0.46$, $\tan^2 \theta_{13} \sim 0$, and $\delta m_{21}^2 \sim 7.1 \times 10^{-5}$ eV$^2$. It is found that the combined solar neutrino and KamLAND date provide the limit $\cos^4 \theta_{13} < 0.8$ at the 90 % confidence level.