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 $ν^{}_α\leftrightarrow \overlineν^{}_β$ (for $α, β= e, μ, τ$) 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 $P(ν^{}_α\to \overlineν^{}_β)$ and $P(\overlineν^{}_α\to ν^{}_β)$ are derived, and the CP asymmetries ${\cal A}^{}_{αβ} \equiv [P(ν^{}_α\to \overlineν^{}_β) - P(\overlineν^{}_α\to ν^{}_β)]/[P(ν^{}_α\to \overlineν^{}_β) + P(\overlineν^{}_α\to ν^{}_β)]$ 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.