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 vP1v over bar P2 -> vP2 no off -diagonal refractive index between v and v over bar of a single flavor of massless neutrinos. For a nonvanishing mass, collective helicity oscillations are possible, representing de facto v - v over bar oscillations in the Majorana case. However, such phenomena are suppressed by the smallness of neutrino masses as discussed in the previous literature. v over bar P1 is helicity suppressed and vanishes for massless neutrinos, implying that there is