We discuss the possibilities of high precision measurement of the solar neutrino mixing angle ${\theta }_{\odot }\equiv {\theta }_{12}$ in solar and reactor neutrino experiments. The improvements in the determination of ${sin}^2{\theta }_{12}$, which can be achieved with the expected increase of statistics and reduction of systematic errors in the currently operating solar and KamLAND experiments, are summarized. The potential of LowNu $\nu -e$ elastic scattering experiment, designed to measure the $pp$ solar neutrino flux, for high precision determination of ${sin}^2{\theta }_{12}$, is investigated in detail. The accuracy in the measurement of ${sin}^2{\theta }_{12}$, which can be achieved in a reactor experiment with a baseline $L\sim (50–70)\mathrm{km}$, corresponding to a survival probability minimum (SPMIN), is thoroughly studied. We include the effect of the uncertainty in the value of ${sin}^2{\theta }_{13}$ in the analyses. A LowNu measurement of the $pp$ neutrino flux with a 1% error would allow to determine ${sin}^2{\theta }_{12}$ with an error of 14% (17%) at $3\sigma$ from a two-generation (three-generation) analysis. The same parameter ${sin}^2{\theta }_{12}$ can be measured with an uncertainty of 2% (6%) at $1\sigma$ ($3\sigma$) in a reactor experiment with $L\sim 60\mathrm{km}$, statistics of $\sim 60$ GWkTy and systematic error of 2%. For the same statistics, the increase of the systematic error from 2% to 5% leads to an increase in the uncertainty in ${sin}^2{\theta }_{12}$ from 6% to 9% at $3\sigma$. The inclusion of the ${sin}^2{\theta }_{13}$ uncertainty in the analysis changes the error on ${sin}^2{\theta }_{12}$ to 3% (9%). The effect of ${sin}^2{\theta }_{13}$ uncertainty on the ${sin}^2{\theta }_{12}$ measurement in both types of experiments is considerably smaller than naively expected.

• Received 28 December 2004

DOI:https://doi.org/10.1103/PhysRevD.72.033013