The non-equivalence of Weyl and Majorana neutrinos with standard-model gauge interactions

It is shown that a Majorana neutrino with identical phenomenology as a standard-model Weyl neutrino obeys a Lagrangian different by a factor √ 2 in the weak-interaction term from the one that follows from the standard model. Assuming that the standard model does hold in good approximation for the weak interactions of a Majorana neutrino e.g. a charged-current production cross section a factor 2 larger than the observed one is predicted. From this it is concluded that the neutrino is not of Majorana type. This conclusion does not forbid the possible existence of a Weyl neutrino with a Majorana mass term and ensuing lepton-number violating phenomena (like e.g. neutrino-less double beta decay). The paper is not in contradiction with any published literature, because it analyses the formal proof of equivalence between Weyl and Majorana neutrino for the first time under the assumption that the standard model is quantitatively correct for the weak interactions of the neutrino.