https://doi.org/10.1140/epjc/s10052-020-7855-4
Regular Article - Theoretical Physics
Operatorial characterization of Majorana neutrinos
Interdisciplinary Theoretical and Mathematical Sciences Program, RIKEN, Wako, 351-0198, Japan
* e-mail: k-fujikawa@riken.jp
Received:
5
November
2019
Accepted:
18
March
2020
Published online:
30
March
2020
The Majorana neutrino 
when constructed as a superposition of chiral fermions such as 
is characterized by 
, and the CP symmetry describes the entire physics contents of Majorana neutrinos. Further specifications of C and P separately could lead to difficulties depending on the choice of C and P. The conventional 
with well-defined P is naturally defined when one constructs the Majorana neutrino from the Dirac-type fermion. In the seesaw model of Type I or Type I+II where the same number of left- and right-handed chiral fermions appear, it is possible to use the generalized Pauli–Gursey transformation to rewrite the seesaw Lagrangian in terms of Dirac-type fermions only; the conventional C symmetry then works to define Majorana neutrinos. In contrast, the “pseudo C-symmetry” 
(and associated “pseudo P-symmetry”), that has been often used in both the seesaw model and Weinberg’s model to describe Majorana neutrinos, attempts to assign a nontrivial charge conjugation transformation rule to each chiral fermion separately. But this common construction is known to be operatorially ill-defined and, for example, the amplitude of the neutrinoless double beta decay vanishes if the vacuum is assumed to be invariant under the pseudo C-symmetry.
© The Author(s), 2020
