Massive particles whose dynamics are described by the free Dirac equation can oscillate between left and right-handed chiral states, undergoing chiral oscillations. The phenomenon is prominent for non-relativistic particles, and can yield a depletion on the expected measured ﬂux of cosmic neutrinos and a modiﬁcation of quantum correlations encoded in lepton-antineutrino pairs. In this context, the interplay between chiral and ﬂavor oscillations plays an important role in the description of neutrino ﬂavor dynamics. In this paper, we extend previous results and obtain ﬂavor oscillation formulas including chiral oscillations for N ﬂavor mixing. We consider the general case of mixing that can distinguish between left and right-handed states and derive the ﬂavor oscillation probabilities for Dirac and Majorana neutrinos within the bispinor formalism. We show that, for three ﬂavors, oscillation probabilities between chiral left and right-handed ﬂavor states allows for distinguishing between Dirac and Majorana neutrinos in the presence of additional CP-violation Majorana phases. To summarize, our work addresses to phenomenologically accessible chiral oscillation eﬀects on non-relativistic neutrino dynamics and on quantum correlations encoded in ﬂavor states.
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