Genuine and Matter-induced Components of the CPV Asymmetry for Neutrino Oscillations

Abstract

These results represent the solution for the historical problem of the contamination by matter effects on the CPV Asymmetry for neutrino oscillations. Vacuum is CPT-symmetric and matter is T-symmetric, the goal is accomplished by using this guiding principle. Independent of the theoretical framework for the dynamics of the active neutrino flavors, we prove the Disentanglement Theorem A(CP)=A(CP, T)+A(CP, CPT) for the experimental CPV Asymmetry, with A(CP, T) genuine T-odd and A(CP, CPT) fake CPT-odd. For the effective Hamiltonian written as the sum of free mass propagation plus the matter potential for electron-neutrinos, the two components have definite parities under the baseline L, the matter potential "a", the imaginary part $\sin\delta$ of the PMNS mixing matrix and the hierarchy "h"=$\pm 1$ in the neutrino mass ordering: A(CP, T) is odd in L and $\sin\delta$ plus even in a and h; A(CP, CPT) is even in L and $\sin\delta$ plus odd in a and almost odd in h. For present terrestrial accelerator sources of muon-neutrinos and antineutrinos, the two components of the appearance CPV asymmetry A(CP) can be disentangled by either baseline dependence (HKK) or energy dependence (DUNE). At the DUNE baseline, the higher energy region above the first oscillation node provides a dominant matter-induced A(CP, CPT) component and the sign of the experimental asymmetry A(CP) gives the hierarchy in the neutrino mass ordering. On the contrary, there is a "magic energy" E around the second oscillation maximum in which the fake A(CP, CPT) component has a first-rank zero whereas the genuine A(CP, T) component has a maximum proportional to sin{\delta}. With a modest energy resolution $\Delta E \sim 200$ MeV an effective zero remains in the matter-induced A(CP, CPT).