Untangling CP violation and the mass hierarchy in long baseline experiments

In the overlap region, for the normal and inverted hierarchies, of the neutrino-antineutrino bi-probability space for ν_μ→ν_e appearance, we derive a simple identity between the solutions in the (sin⁡²2θ₁₃, sin⁡δ) plane for the different hierarchies. The parameter sin⁡²2θ₁₃ sets the scale of the ν_μ→ν_e appearance probabilities at the atmospheric δm_atm²≈2.4×10^-3  eV² whereas sin⁡δ controls the amount of CP violation in the lepton sector. The identity between the solutions is that the difference in the values of sin⁡δ for the two hierarchies equals twice the value of √sin⁡²2θ₁₃ divided by the critical value of √sin⁡²2θ₁₃. We apply this identity to the two proposed long baseline experiments, T2K and NOvA, 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. This identity demonstrates the true complementarity of T2K and NOvA.