The phenomenology of neutrinos with Majorana mass terms and standard-model interactions derived in the charge-parity basis

Abstract

(abridged) The physical mechanisms that make a neutrino with standard-model (SM) weak interactions a "lepton-number conservation (LNC) violating" neutrino such as the Majorana neutrino are analysed in a basis of two Majorana states that have opposite charge-parity ("charge-parity basis"). A small Majorana mass that is larger than any Dirac mass makes the neutrino not a Majorana but a "pseudo-Majorana" particle that has no definite chirality and therefore has a different phenomenology than the physical neutrino. A combination of a large Majorana and Dirac mass of nearly equal value makes the neutrino a Majorana neutrino. However if this Majorana neutrino has SM interactions, its weak transition amplitudes squared are a factor 2 smaller than the ones observed for the physical neutrino. Only with a small Dirac mass that is larger than any Majorana mass (and in the massless case), the physical neutrino's phenomenology is correctly predicted by the SM. Such a mass combination makes the neutrino a Dirac- or (the most likely possibility for the physical neutrino) Pontecorvo's pseudo-Dirac particle which features neutrino-antineutrino oscillations, that violate LNC. Pseudo-Dirac neutrinos enable a completely negligible rate for neutrinoless double-beta decay if there is no Majorana-mass independent decay mechanism. Off-diagonal components of the mass matrix in the charge-parity basis make the neutrino a mixture of Dirac field with a different particle and anti-particle mass (i.e. a mass that violates CPT invariance) and a pseudo-Dirac field. Such a neutrino leads to a phenomenology similar to the one with additional generations of sterile neutrinos.