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 ${\mathcal{A}}_{\alpha \beta }^{}\equiv [P({\nu }_{\alpha }^{}\to {\overline{\nu }}_{\beta }^{})-P({\overline{\nu }}_{\alpha }^{}\to {\nu }_{\beta }^{})]/[P({\nu }_{\alpha }^{}\to {\overline{\nu }}_{\beta }^{})+P({\overline{\nu }}_{\alpha }^{}\to {\nu }_{\beta }^{})]$ 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.

Comments: 26 pages, 1 figure, 2 tables, more discussions and references added, accepted by PLB