Is realization of Majorana neutrino and neutrinoless double beta decay possible in the framework of standard weak interactions?

Abstract

Usually it is supposed that Majorana neutrino produced in the superposition state χ L = ν L + (ν L ) c and then follows the neutrinoless double beta decay. But since the standard weak interactions are chiral invariant then neutrino at production has definite helicity (ν L and (ν L ) c have opposite spirality). Then these neutrinos are separately produced and their superposition state cannot appear. Thus we see that for unsuitable helicity the neutrinoless double β decay is not possible even if it is supposed that neutrino is a Majorana particle (i.e. there is not a lepton number which is conserved). Also transition of Majorana neutrino ν L into antineutrino (ν L ) c at their oscillations is forbidden since helicity in vacuum holds. Transition Majora neutrino ν L into (ν R ) c (i.e., ν L → (ν R ) c ) at oscillations is unobserved since it is supposed that mass of (ν R ) c is very big. If neutrino is a Dirac particle there can be transition of ν L neutrino into (sterile) antineutrino \( \bar v_R \) (i.e., ν L → \( \bar v_R \)) at neutrino oscillations if there takes place double violation of lepton number. It is necessary also to remark that introducing of a Majorana neutrino implies violation of global and local gauge invariance in the standard weak interactions.