Exploring the sensitivity of current and future experiments toθ⊙

The first results from the KamLAND experiment in conjunction with the global solar neutrino data have demonstrated the striking ability to constrain the $\Delta m_{\odot }^2\left(\Delta m_{21}^2\right)$ very precisely. However the allowed range of ${\theta }_{\odot }\left({\theta }_{12}\right)$ did not change much with the inclusion of the KamLAND results. In this paper we probe if future data from KamLAND can increase the accuracy of the allowed range in ${\theta }_{\odot }$ and conclude that even after 3 kton yr of statistics and with the most optimistic error estimates, KamLAND may find it hard to significantly improve the bounds on the mixing angle obtained from the solar neutrino data. We discuss the ${\theta }_{12}$ sensitivity of the survival probabilities in matter (vacuum) as relevant for the solar (KamLAND) experiments. We find that the presence of matter effects in the survival probabilities for ${}^8\mathrm{B}$ neutrinos gives the solar neutrino experiments SK and SNO an edge over KamLAND, as far as ${\theta }_{12}$ sensitivity is concerned, particularly near the maximal mixing. Among solar neutrino experiments we identify SNO as a most promising candidate for constraining ${\theta }_{12}$ and make a projected sensitivity test for the mixing angle by reducing the error in the neutral current measurement at SNO. Finally, we argue that the most accurate bounds on ${\theta }_{12}$ can be achieved in a reactor experiment, if the corresponding baseline and energy can be tuned to a minimum in the survival probability. We propose a new reactor experiment that can give the value of ${\tan }^2{\theta }_{12}$ to within 14%. We also discuss the future Borexino and LowNu experiments.