High Precision Measurements of ${\theta }_{\odot }$ in Solar and Reactor Neutrino Experiments

Abstract

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 summarised. 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 $L\sim (50-70)$ 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 $L\sim 60$ 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.

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