The Sensitivity of SNO+ to $\Delta m_{12}^{2}$ Using Reactor Anti-neutrino Data

Insofar as the detection of anti-neutrinos from nuclear reactors is concerned, the SNO+ detector -- a 1 kilo-tonne liquid scintillator detector that inherits the experimental infrastructure from the recently finished SNO experiment -- is expected to perform just as well as the KamLAND experiment. The most important difference between these experiments is the distribution of nuclear reactors: whereas KamLAND has 9 nuclear reactor sites within 300 km with a flux-averaged baseline of about 180 km, SNO+ has only 1 within 300 km, with an average baseline of $\approx 750$ km. As a result, the reactor anti-neutrino flux at SNO+ is only about 1/5 that at KamLAND, and the ability of SNO+ to constrain the solar neutrino oscillation parameter is diminished by a factor of about $\sqrt{1/5} = 1/2.2$ relative to KamLAND. In spite of this, SNO+ has comparable sensitivity to $\Delta m^{2}_{12}$ as KamLAND because the rate of change of the spectral distortion as a function of this parameter is much greater than for KamLAND. In this report, this advantage is examined quantitatively using a geometric approximation that makes clear how the shape from SNO+ has more statistical power than that from KamLAND. This result then is confirmed by determining the sensitivity to $\Delta m^{2}_{12}$ using an ensemble experiment technique.