Collective neutrino-antineutrino oscillations in dense neutrino environments?

The paradigm-changing possibility of collective neutrino-antineutrino oscillations was recently advanced in analogy to collective flavor oscillations. However, the amplitude for the backward scattering process ${\nu }_{{\mathbf{p}}_1}{\bar{\nu }}_{{\mathbf{p}}_2}\to {\nu }_{{\mathbf{p}}_2}{\bar{\nu }}_{{\mathbf{p}}_1}$ is helicity-suppressed and vanishes for massless neutrinos, implying that there is no off-diagonal refractive index between $\nu$ and $\bar{\nu }$ of a single flavor of massless neutrinos. For a nonvanishing mass, collective helicity oscillations are possible, representing de-facto $\nu$–$\bar{\nu }$ oscillations in the Majorana case. However, such phenomena are suppressed by the smallness of neutrino masses as discussed in the previous literature.