A Majorana particle is a fermion whose antiparticle is itself. In other words, a Majorana fermion has only two components, rather than 4 components for a Dirac fermion. Neutrinos are alleged as possibly Majorana fermions in most text books.
However with the observation of neutrino oscillations, it's known that neutrinos do possess masses, either Dirac or Majorana masses (or most likely both, required by the seesaw mechanism to account for the smallness of neutrino masses). Either case indicates the existence of right-handed (RH) neutrinos in addition to the left-handed (LH) neutrinos (hence there are 4 independent components for neutrinos, invalidating the Majorana neutrino hypothesis), since:
- Dirac mass couples LH neutrinos with RH neutrinos.
- Majorana mass is only allowed for sterile fermions, such as RH neutrinos. Whereas LH neutrinos participate in weak interactions, thus could not directly carry Majorana mass (unless one is willing to introduce the non-renormalizable Weinberg operator to beget the Majorana mass term via the VEV of the Higgs field, as noted by Cosmas Zachos), which would explicitly violate the electroweak symmetries. In the case of Majorana neutrino, the antiparticles of LH neutrinos are still involved in weak interactions, even though they are purported as RH. The Wikipedia page on Neutrino Oscillation espouses the false claim (is introducing non-renormalizability the smallest modification?) that "The smallest modification to the Standard Model, which only has left-handed neutrinos, is to allow these left-handed neutrinos to have Majorana masses".
So with the observation of neutrino oscillations since 20 years ago (dated back to 1998), why is the notion of neutrinos as possiblly Majorana fermions still promoted?