‘Majorana Mass’ Fermions as Untrue Majorana Particles, Rather Endowed with Pseudoscalar-Type Charges than Genuinely Neutral

Abstract

The idea of a ‘Majorana mass’ to make a chiral neutrino really neutral is here reconsidered. It is pointed out that such an approach, unlike Majorana’s (non-chiral) old one, does not strictly lead, in general, to a true self-conjugate particle. This can be seen on directly using the basic definition (or fundamental representation) of charge conjugation C in Quantum Field Theory, as an operation just acting on annihilation and creation operators and just expressing particle–antiparticle interchange. It is found, indeed, that the ‘active’ and ‘sterile’ whole fields which can be obtained from mixing the chiral components of two mutually charge-conjugate Dirac fields are themselves ‘charge conjugate’ to each other (rather than individually self-conjugate). These fields, taken as mass eigenfields (as in the ‘Majorana mass’ case), are shown to describe particles carrying pseudoscalar-type charges and being neutral relative to scalar-type charges only. For them, ‘CP symmetry’ would be nothing but pure mirror symmetry, and C violation (already implied in their respective ‘active’ and ‘sterile’ behaviors) should then involve time-reversal violation as well. The new (no longer strictly chargeless) ‘Majorana mass’ neutrino model still proves, however, neither to affect the usual expectation for a neutrinoless double β-decay, nor to prevent ‘active’ and ‘sterile’ neutrino varieties from generally taking different mass values. One has, on the other hand, that any fermion being just a genuine (i.e. really self-conjugate) Majorana particle cannot truly exist in two distinct—‘active’ and ‘sterile’—versions, and it can further bear only a unified mass kind which may at once be said to be either a ‘Majorana-like’ or a ‘Dirac-like’ mass kind.