From parameter space constraints to the precision determination of the leptonic Dirac CP phase

We discuss the precision determination of the leptonic Dirac CP phase$\delta_{CP}$ in neutrino oscillation experiments, where we apply the conceptof ``CP coverage''. We demonstrate that this approach carries more informationthan a conventional CP violation measurement, since it also describes theexclusion of parameter regions. This will be very useful for next-generationlong baseline experiments where for sizable $\sin^2 2 \theta_{13}$ firstconstraints on $\delta_{CP}$ can be obtained. As the most sophisticatedexperimental setup, we analyze neutrino factories, where we illustrate themajor difficulties in their analysis. In addition, we compare their potentialto the one of superbeam upgrades and next-generation experiments, which alsoincludes a discussion of synergy effects. We find a strong dependence on theyet unknown true values of $\sin^2 2 \theta_{13}$ and $\delta_{CP}$, as well asa strong, non-Gaussian dependence on the confidence level. A systematicunderstanding of the complicated parameter dependence will be given. Inaddition, it is shown that comparisons of experiments and synergy discussionsdo in general not allow for an unbiased judgment if they are only performed atselected points in parameter space. Therefore, we present our results independence of the yet unknown true values of $\sin^2 2 \theta_{13}$ and$\delta_{CP}$. Finally we show that for $\delta_{CP}$ precision measurementsthere exist simple strategies including superbeams, reactor experiments,superbeam upgrades, and neutrino factories, where the crucial discriminator is$\sin^2 2 \theta_{13} \sim 10^{-2}$.Comment: 32 pages, 9 figure