Disentangling Genuine from Matter-Induced CP Violation in Neutrino Oscillations

We prove that, in any flavor transition, neutrino oscillation CP-violating asymmetries in matter have two disentangled components: (i) a CPT-odd T-invariant term, non-vanishing iff there are interactions with matter, and (ii) a T-odd CPT-invariant term, non-vanishing iff there is genuine CP violation. As function of the baseline, these two terms are distinct L-even and L-odd observables to separately test (i) matter effects sensitive to the neutrino hierarchy and (ii) genuine CP violation in the neutrino sector. For the golden ν_{μ}→ν_{e} channel, the different energy distributions of the two components provide a signature of their separation. At long baselines, they show oscillations in the low and medium energy regions, with zeros at different positions and peculiar behavior around the zeros. We discover a magic energy E=(0.91±0.01)  GeV at L=1300  km with vanishing CPT-odd component and maximal genuine CP asymmetry proportional to sinδ, with δ the weak CP phase. For energies above 1.5 GeV, the sign of the CP asymmetry discriminates the neutrino hierarchy.