Untangling CP Violation and the Mass Hierarchy in Long Baseline Experiments

Abstract

In the overlap region, for the normal and inverted hierarchies, of the neutrino-antineutrino bi-probability space for ${\nu }_{\mu }\to {\nu }_e$ appearance, we derive a simple identity between the solutions in the (${\sin }^{2}2{\theta }_{13}$, $\sin \delta$) plane for the different hierarchies. The parameter ${\sin }^{2}2{\theta }_{13}$ sets the scale of the ${\nu }_{\mu }\to {\nu }_e$ appearance probabilities at the atmospheric $\delta m_{atm}^2\approx 2.4\times 10^{-3}$ eV${}^2$ whereas $\sin \delta$ controls the amount of CP violation in the lepton sector. The identity between the solutions is that the difference in the values of $\sin \delta$ for the two hierarchies equals twice the value of $\sqrt{{\sin }^{2}2{\theta }_{13}}$ divided by the {\it critical} value of $\sqrt{{\sin }^{2}2{\theta }_{13}}$. We apply this identity to the two proposed long baseline experiments, T2K and NO$\nu$A, and we show how it can be used to provide a simple understanding of when and why fake solutions are excluded when two or more experiments are combined. The identity demonstrates the true complimentarity of T2K and NO$\nu$A.

15 pages, Latex, 4 postscript figures. Submitted to New Journal of Physics, ``Focus on Neutrino Physics'' issue

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• Non-adiabatic Level Crossing in Resonant Neutrino Oscillations

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