Neutrino Oscillations in the Precision Era

With the discovery of a modest size for the mixing angle $\theta_{13} \sim 9^\circ$ by the Daya Bay collaboration at $>$5 sigma (\cite{dayabay}) the science of neutrino oscillations has shifted to explicit demonstration of CP violation and precision determination of the CP phase in the 3-flavor framework. Any additional contributions from new physics to the oscillation channel $\nu_\mu \to \nu_e$ could be uncovered by multiple constraints in the ($\theta_{13}, \delta_{CP}$) parameter space. In long-baseline experiments such constraints will require examination of the oscillation strength at higher $L/E$ where the effects of CP violation will be large. For the fixed baseline of 1300 km for the Long-Baseline Neutrino Experiment (LBNE, Fermilab to Homestake), it will be important to examine oscillations at low energies ($<1.5$ GeV) with good statistics, low backgrounds, and excellent energy resolution. The accelerator upgrades in the Project-X era have the potential to offer the beams of the needed intensity and quality for this advanced science program. In this paper we examine the event rates for high intensity, low energy running of Project-X and the Fermilab Main Injector complex, and the precision in the ($\theta_{13}, \delta_{CP}$) space. In this paper we have examined the baseline distance of 1300 km in detail, however we point out that much longer distances such as 2500 km should also be exmained with a beam from FNAL in light of the new understanding of the neutrino mixing.