Abstract
The idea that the Majorana neutrino should be identified as a Bogoliubov quasiparticle is applied to the seesaw mechanism for the three generations of neutrinos in the Standard Model. A relativistic analogue of the Bogoliubov transformation in the present context is a CP-preserving canonical transformation but modifies charge conjugation properties in such a way that the C-noninvariant fermion number violating term (condensate) is converted to a Dirac mass term. Puzzling aspects associated with the charge conjugation of chiral Weyl fermions are clarified. By invoking the Coleman--Weinberg mechanism in the framework of dimensional regularization, it is also noted that seesaw models become unnatural in some parameter regions which induce the hierarchy problems in the bosonic sector.
Highlights
We have recently witnessed a remarkable progress in neutrino physics [1]
Which is required to define the Majorana fermion in the seesaw mechanism, changes at the same time the chirality of the neutrino [2,3,4,5]. This definition leads to many puzzling results [10]. Those contradictions are resolved if one uses a relativistic analog of Bogoliubov transformation, which is a canonical transformation and converts a C-noninvariant fermion-number condensate to a Dirac mass, and we suggested the idea that the Majorana neutrino should be identified as the first Bogoliubov quasiparticle among elementary particles [11]
We have identified the Majorana neutrinos in the seesaw model as Bogoliubov quasiparticles in a natural manner by extending the analysis of a relativistic analog of the Bogoliubov transformation to the three generations of neutrinos, when C and P are violated with mR ≠ mL
Summary
We have recently witnessed a remarkable progress in neutrino physics [1]. Those achievements in experimental and theoretical studies of neutrino physics are nicely summarized in many textbooks and reviews, for example, Refs. [2,3,4,5,6]. A relativistic analog of the Bogoliubov transformation, which converts a C-noninvariant fermion-number “condensate” to a Dirac mass and changes the charge conjugation properties of vacuum, is shown to be crucial to understand the Majorana neutrinos in a logically consistent manner. Which is required to define the Majorana fermion in the seesaw mechanism, changes at the same time the chirality (helicity) of the neutrino [2,3,4,5] This definition leads to many puzzling results [10]. Those contradictions are resolved if one uses a relativistic analog of Bogoliubov transformation, which is a canonical transformation and converts a C-noninvariant fermion-number condensate to a Dirac mass, and we suggested the idea that the Majorana neutrino should be identified as the first Bogoliubov quasiparticle among elementary particles [11]. We are going to explain how the C-violating Lagrangian (5) can consistently describe Majorana neutrinos which are the exact eigenstates of C symmetry
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