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Usually it is supposed that Majorana neutrino produced in the superpositionstate $\chi_L = \nu_L + (\nu_L)^c$ and then follows the neutrinoless doublebeta decay. But since weak interactions are chiral invariant then the neutrinoat production has definite helicity (i.e., $\nu_L$ and $(\nu_L)^c$ neutrinosare separately produced and then neutrino is not in the superposition state).This helicity cannot change after production without any external interactions.Thus we see that for unsuitable helicity the neutrinoless double $\beta$ decayis not possible even if neutrino is a Majorana particle. Also transition ofMajorana neutrino into antineutrino at their oscillations is forbidden sincehelicity in vacuum holds. Then only possibility to prove that neutrino is aDirac but not Majorana particle is detection transition of $\nu_L$ neutrinointo (sterile) antineutrino $\bar\nu_R$ (i.e., $\nu_L \to \bar\nu_R$) atneutrino oscillations. Transition Majora neutrino $\nu_L$ into $(\nu_R)^c$(i.e., $\nu_L \to (\nu_R)^c$) at oscillations is unobserved since it issupposed that mass of $(\nu_R)^c$ is very big.

Majorana neutrino. Is double neutrinoless beta decay possible in the  framework of the weak interactions? How to prove that neutrino is Majorana  particle