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.