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.