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 ν_p1ν_¯p2→ν_p2ν_¯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.