Seesaw mechanism and pseudo C-symmetry

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Fujikawa , K & Tureanu , A 2019 , ' Seesaw mechanism and pseudo C-symmetry ' , European Physical Journal C. Particles and Fields , vol. 79 , no. 9 , 752 .

Title: Seesaw mechanism and pseudo C-symmetry
Author: Fujikawa, Kazuo; Tureanu, Anca
Contributor: University of Helsinki, RIKEN
University of Helsinki, Department of Physics
Date: 2019-09-10
Number of pages: 8
Belongs to series: European Physical Journal C. Particles and Fields
ISSN: 1434-6052
Abstract: It is shown that the specific “charge conjugation” transformation used to define the Majorana fermions in the conventional seesaw mechanism, namely $$(\nu _{R})^{C}=C\overline{\nu _{R}}^{T}$$(νR)C=CνR¯Tfor a chiral fermion $$\nu _{R}$$νR(and similarly for $$\nu _{L}$$νL), is a hidden symmetry associated with CP symmetry, and thus it formally holds independently of the P- and C-violating terms in the CP invariant Lagrangian and it is in principle applicable to charged leptons and quarks as well. This hidden symmetry, however, is not supported by a consistent unitary operator and thus it leads to mathematical (operatorial) ambiguities. When carefully examined, it also fails as a classical transformation law in a Lorentz invariant field theory. To distinguish it from the standard charge conjugation symmetry, we suggest for it the name of pseudo C-symmetry. The pseudo C-symmetry is effective to identify Majorana neutrinos analogously to the classical Majorana condition. The analysis of CP breaking in weak interactions is performed using the conventional CP transformation, which is defined independently of the pseudo C-transformation, in the seesaw model after mass diagonalization. A way to ensure an operatorially consistent formulation of C-conjugation is to formulate the seesaw scheme by invoking a relativistic analogue of the Bogoliubov transformation.
Subject: 114 Physical sciences

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