Non-unitary Leptonic Flavor Mixing and CP Violation in Neutrino-antineutrino Oscillations

Abstract: If massive neutrinos are Majorana particles, then the lepton number should be violated in nature and neutrino-antineutrino oscillations $\nu^{}_\alpha \leftrightarrow \overline{\nu}^{}_\beta$ (for $\alpha, \beta = e, \mu, \tau$) will definitely take place. In the present paper, we study the properties of CP violation in neutrino-antineutrino oscillations with the non-unitary leptonic flavor mixing matrix, which is actually a natural prediction in the canonical seesaw model due to the mixing between light and heavy Majorana neutrinos. The oscillation probabilities $P(\nu^{}_\alpha \to \overline{\nu}^{}_\beta)$ and $P(\overline{\nu}^{}_\alpha \to \nu^{}_\beta)$ are derived, and the CP asymmetries ${\cal A}^{}_{\alpha \beta} \equiv [P(\nu^{}_\alpha \to \overline{\nu}^{}_\beta) - P(\overline{\nu}^{}_\alpha \to \nu^{}\beta)]/[P(\nu^{}\alpha \to \overline{\nu}^{}_\beta) + P(\overline{\nu}^{}_\alpha \to \nu^{}_\beta)]$ are also calculated. Taking into account current experimental bounds on the leptonic unitarity violation, we show that the CP asymmetries induced by the non-unitary mixing parameters can significantly deviate from those in the limit of a unitary leptonic flavor mixing.