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; 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 $\nu_\mu \to \nu_e$ channel, the different energy distributions of the two components provide a signature of their separation. At long baselines, they show oscillations in the low energy region, with zeros at different positions and peculiar behavior around the zeros. We discover a magic energy $E = (0.91 \pm 0.01)$ GeV at L = 1300 km with vanishing CPT-odd term and maximal genuine CP asymmetry proportional to $\sin\delta$, with $\delta$ the weak CP phase. For energies above 1.5 GeV, the sign of the CP asymmetry discriminates the neutrino hierarchy.