UntanglingCPviolation 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→νₑ appearance, we derive a simple identity between the solutions in the (sin²2θ₁₃, sinδ) plane for the different hierarchies. The parameter sin²2θ₁₃ sets the scale of the ν_μ→νₑ appearance probabilities at the atmospheric δmₐₜₘ²≈2.4×10^-3 eV² whereas sinδ controls the amount of $CP$ violation in the lepton sector. The identity between the solutions is that the difference in the values of sinδ for the two hierarchies equals twice the value of √sin²2θ₁₃ divided by the critical value of √sin²2θ₁₃. 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.