Large $\nu$-$\bar{\nu}$ Oscillations from High-Dimensional Lepton Number Violating Operator

It is usually believed that the observation of the neutrino-antineutrino (${\nu}$-$\bar{\nu}$) oscillations is almost impossible since the oscillation probabilities are expected to be greatly suppressed by the square of tiny ratio of neutrino masses to energies. Such an argument is applicable to most models for neutrino mass generation based on the Weinberg operator, including the seesaw models. However, in the present paper, we shall give a counterexample to this argument, and show that large $\nu$-$\bar{\nu}$ oscillation probabilities can be obtained in a class of models in which both neutrino masses and neutrinoless double beta ($0\nu\beta\beta$) decays are induced by the high-dimensional lepton number violating operator ${\cal O}_7 = \bar{u}_R l^c_R \bar{L}_L H^*d_R + {\rm H.c.}$ with $u$ and $d$ representing the first two generations of quarks. In particular, we find that the predicted $0\nu\beta\beta$ decay rates have already placed interesting constraints on the $\nu_e \leftrightarrow \bar{\nu}_e$ oscillation. Moreover, we provide an UV-complete model to realize this scenario, in which a dark matter candidate naturally appears due to the new $U(1)_d$ symmetry.