If the massive neutrinos are identified to be the Majorana particles via a convincing measurement of the neutrinoless double beta ($0\nu \beta \beta$) decay, how to determine the Majorana $CP$-violating phases in the $3\times 3$ lepton flavor mixing matrix $U$ will become a desirable experimental question. The answer to this question is to explore all the possible lepton-number-violating (LNV) processes in which the Majorana phases really matter. In this paper we carry out a systematic study of $CP$ violation in neutrino-antineutrino oscillations, whose $CP$-conserving parts involve six independent $0\nu \beta \beta$-like mass terms $⟨m{⟩}_{\alpha \beta }$ and $CP$-violating parts are associated with nine independent Jarlskog-like parameters ${\mathcal{V}}_{\alpha \beta }^{ij}$ (for $\alpha$, $\beta =e$, $\mu$, $\tau$ and $i$, $j=1$, 2, 3). With the help of current neutrino oscillation data, we analyze the sensitivities of $|⟨m{⟩}_{\alpha \beta }|$ and ${\mathcal{V}}_{\alpha \beta }^{ij}$ to the three $CP$-violating phases of $U$, and illustrate the salient features of six independent $CP$-violating asymmetries between ${\nu }_{\alpha }\to {\overline{\nu }}_{\beta }$ and ${\overline{\nu }}_{\alpha }\to {\nu }_{\beta }$ oscillations. As a by-product, the effects of the $CP$-violating phases on the LNV decays of doubly and singly charged Higgs bosons are reexamined by taking account of the unsuppressed value of ${\theta }_{13}$. Such $CP$-conserving LNV processes can be complementary to the possible measurements of neutrino-antineutrino oscillations in the distant future.

• Received 29 May 2013

DOI:https://doi.org/10.1103/PhysRevD.88.033002