Naturalness in see-saw mechanism and Bogoliubov transformation

TL;DR

This paper offers a new perspective on the see-saw mechanism by applying a Bogoliubov transformation, revealing a natural explanation for Majorana neutrinos and highlighting a fine-tuning issue in typical models.

Contribution

It introduces an alternative view of the see-saw mechanism using Bogoliubov transformation, clarifying Majorana neutrino emergence and identifying a fine-tuning problem.

Findings

Majorana neutrinos naturally emerge with strong C violation.

A fine-tuning of 10^{-15} to 10^{-26} is needed for naturalness in typical models.

The see-saw mechanism requires precise parameter adjustments to avoid small couplings.

Abstract

We present an alternative perspective on the see-saw mechanism for the neutrino mass, according to which the small neutrino mass is given as a difference of two large masses. This view emerges when an analogue of the Bogoliubov transformation is used to describe Majorana neutrinos in the Lagrangian of the see-saw mechanism, which is analogous to the BCS theory. The Bogoliubov transformation clarifies the natural appearance of Majorana fermions when C is strongly violated by the right-handed neutrino mass term with good CP in the single flavor model. Analyzing typical models with $m_{R}$= $10^{4}$ to $10^{15}$ GeV, it is shown that a hitherto unrecognized fine tuning of the order $m_{\nu}/m_{R}=10^{-15}$ to $10^{-26}$ is required to make the commonly perceived see-saw mechanism work in a natural setting, namely, when none of dimensionless coupling constants are very small.