'Majorana mass' fermions as untrue Majorana particles, rather endowed with pseudoscalar-type charges than genuinely neutral

TL;DR

This paper reevaluates the concept of Majorana mass for neutrinos, showing that such particles are not truly neutral but carry pseudoscalar charges, affecting their symmetry properties and the interpretation of neutrino types.

Contribution

It demonstrates that Majorana mass fields are charge conjugate to each other and carry pseudoscalar charges, challenging the traditional notion of truly neutral Majorana particles.

Findings

Majorana mass fields carry pseudoscalar charges.

Active and sterile neutrinos can have different masses.

Majorana particles cannot be truly self-conjugate in two distinct forms.

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 $\beta$-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.