Majorana neutrinos in seesaw mechanism and Bogoliubov quasiparticles

TL;DR

This paper explores the identification of Majorana neutrinos as Bogoliubov quasiparticles within the seesaw mechanism, revealing how a relativistic transformation affects charge conjugation and discussing implications for model naturalness and hierarchy problems.

Contribution

It introduces a relativistic Bogoliubov transformation framework for Majorana neutrinos in the seesaw mechanism, clarifying charge conjugation issues and analyzing model naturalness.

Findings

Charge conjugation properties are modified by the transformation.

Seesaw models can become unnatural in certain parameter regions.

Hierarchy problems are discussed in the context of the Coleman--Weinberg mechanism.

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.