Understanding CP phase-dependent measurements at neutrino superbeams in terms of bi-rate graphs

We discuss the impact of the true value of the CP phase on the mass hierarchy, CP violation, and CP precision measurements at neutrino superbeams. Useful tools to investigate this impact semi-quantitatively are bi-rate graphs. Unlike bi-probability graphs, which use oscillation probabilities, bi-rate graphs show the total event rates of two measurements simultaneously as a function of the CP phase. Since they allow error bars for direct quantitative estimates, we use bi-rate graphs for a direct comparison with a complete statistical experiment simulation including spectral information, systematics, correlations, and degeneracies. We find that one can describe the CP phase dependencies of the mentioned measurements as well as one can understand the role of the sgn(∆m31)-degeneracy. As one of the most interesting results, we discuss the dependence of the CP precision measurement as a function of the CP phase itself, which leads to “CP patterns”. It turns out that this dependence is rather strong, which means that one has to be careful when one is comparing the CP precisions of different experiments. In addition, we demonstrate that alternative options for a NuMI off-axis antineutrino running, a larger detector size, or a different baseline can also be understood in terms of bi-rate graphs, and we investigate the potential of the first-generation superbeams with respect to the mass hierarchy and CP measurements. Email: [email protected]