Signatures of the genuine and matter-induced components of the CP violation asymmetry in neutrino oscillations

CP asymmetries for neutrino oscillations in matter can be disentangled into the matter-induced CPT-odd (T-invariant) component and the genuine T-odd (CPT-invariant) component. For their understanding in terms of the relevant ingredients, we develop a new perturbative expansion in both $\Delta m^2_{21},\, |a| \ll |\Delta m^2_{31}|$ without any assumptions between $\Delta m^2_{21}$ and $a$, and study the subtleties of the vacuum limit in the two terms of the CP asymmetry, moving from the CPT-invariant vacuum limit $a \to 0$ to the T-invariant limit $\Delta m^2_{21} \to 0$. In the experimental region of terrestrial accelerator neutrinos, we calculate their approximate expressions from which we prove that, at medium baselines, the CPT-odd component is small and nearly $\delta$-independent, so it can be subtracted from the experimental CP asymmetry as a theoretical background, provided the hierarchy is known. At long baselines, on the other hand, we find that (i) a Hierarchy-odd term in the CPT-odd component dominates the CP asymmetry for energies above the first oscillation node, and (ii) the CPT-odd term vanishes, independent of the CP phase $\delta$, at $E =0.92~\mathrm{GeV}\,(L/1300~\mathrm{km})$ near the second oscillation maximum, where the T-odd term is almost maximal and proportional to $\sin\delta$. A measurement of the CP asymmetry in these energy regions would thus provide separate information on (i) the neutrino mass ordering, and (ii) direct evidence of genuine CP violation in the lepton sector.