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 νp1ν¯p2→νp2ν¯p1 is helicity suppressed and vanishes for massless neutrinos, implying that there is no off-diagonal refractive index between ν and ν¯ of a single flavor of massless neutrinos. For a nonvanishing mass, collective helicity oscillations are possible, representing de facto ν-ν¯ oscillations in the Majorana case. However, such phenomena are suppressed by the smallness of neutrino masses as discussed in the previous literature.