Majorana neutrino and the vacuum of Bogoliubov quasiparticle

TL;DR

This paper explores the vacuum structure of Majorana neutrinos as Bogoliubov quasiparticles, revealing a condensate structure analogous to the Nambu--Jona-Lasinio model, and clarifies the C violation in the seesaw mechanism.

Contribution

It introduces a detailed vacuum structure for Majorana neutrinos as Bogoliubov quasiparticles, linking C violation to a condensate in the seesaw mechanism.

Findings

Constructed explicit vacuum form for Majorana neutrinos as Bogoliubov quasiparticles

Identified condensate structure analogous to Nambu--Jona-Lasinio vacuum

Clarified the role of C violation in the vacuum of neutrinos

Abstract

The Lagrangian of the seesaw mechanism is C violating but the same Lagrangian when re-written in terms of Majorana neutrinos is manifestly C invariant. To resolve this puzzling feature, a relativistic analogue of Bogoliubov transformation, which preserves CP but explicitly breaks C and P separately, was introduced together with the notions of a Bogoliubov quasiparticle and an analogue of the energy gap in BCS theory. The idea of Majorana neutrino as Bogoliubov quasiparticle was then suggested. In this paper, we study the vacuum structure of the Bogoliubov quasiparticle which becomes heavy by absorbing the C-breaking. By treating an infinitesimally small C violating term as an analogue of the chiral symmetry breaking nucleon mass in the model of Nambu and Jona-Lasinio, we construct an explicit form of the vacuum of the Bogoliubov quasiparticle which defines Majorana neutrinos in seesaw mechanism. The vacuum of the Bogoliubov quasiparticle thus constructed has an analogous condensate structure as the vacuum of the quasiparticle (nucleon) in the Nambu--Jona-Lasinio model.