High precision measurements ofθ⊙in the solar and reactor neutrino experiments

Abstract

We discuss the possibilities of high precision measurement of the solar neutrino mixing angle ${\ensuremath{\theta}}_{\ensuremath{\bigodot}}\ensuremath{\equiv}{\ensuremath{\theta}}_{12}$ in solar and reactor neutrino experiments. The improvements in the determination of ${sin}^{2}{\ensuremath{\theta}}_{12}$, 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 $\ensuremath{\nu}\ensuremath{-}e$ elastic scattering experiment, designed to measure the $pp$ solar neutrino flux, for high precision determination of ${sin}^{2}{\ensuremath{\theta}}_{12}$, is investigated in detail. The accuracy in the measurement of ${sin}^{2}{\ensuremath{\theta}}_{12}$, which can be achieved in a reactor experiment with a baseline $L\ensuremath{\sim}(50\char21{}70)\text{ }\text{ }\mathrm{km}$, corresponding to a survival probability minimum (SPMIN), is thoroughly studied. We include the effect of the uncertainty in the value of ${sin}^{2}{\ensuremath{\theta}}_{13}$ in the analyses. A LowNu measurement of the $pp$ neutrino flux with a 1% error would allow to determine ${sin}^{2}{\ensuremath{\theta}}_{12}$ with an error of 14% (17%) at $3\ensuremath{\sigma}$ from a two-generation (three-generation) analysis. The same parameter ${sin}^{2}{\ensuremath{\theta}}_{12}$ can be measured with an uncertainty of 2% (6%) at $1\ensuremath{\sigma}$ ($3\ensuremath{\sigma}$) in a reactor experiment with $L\ensuremath{\sim}60\text{ }\text{ }\mathrm{km}$, statistics of $\ensuremath{\sim}60$ 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 ${sin}^{2}{\ensuremath{\theta}}_{12}$ from 6% to 9% at $3\ensuremath{\sigma}$. The inclusion of the ${sin}^{2}{\ensuremath{\theta}}_{13}$ uncertainty in the analysis changes the error on ${sin}^{2}{\ensuremath{\theta}}_{12}$ to 3% (9%). The effect of ${sin}^{2}{\ensuremath{\theta}}_{13}$ uncertainty on the ${sin}^{2}{\ensuremath{\theta}}_{12}$ measurement in both types of experiments is considerably smaller than naively expected.