The Friedberg-Lee Symmetry and Minimal Seesaw Model

TL;DR

This paper explores how the Friedberg-Lee symmetry constrains neutrino mass models, reducing a three-generation seesaw model to a minimal two right-handed neutrino model with a zero light neutrino mass.

Contribution

It demonstrates that applying the Friedberg-Lee symmetry to the seesaw model simplifies it to a minimal form with only two right-handed neutrinos and predicts a massless light neutrino.

Findings

Reduces three-generation seesaw to two right-handed neutrinos

Predicts one light neutrino mass must be zero

Provides symmetry-based constraints on neutrino mass models

Abstract

The Friedberg-Lee (FL) symmetry is generated by a transformation of a fermionic field $q$ to $q + \xi z$. This symmetry puts very restrictive constraints on allowed terms in a Lagrangian. Applying this symmetry to $N$ fermionic fields, we find that the number of independent fields is reduced to $N-1$ if the fields have gauge interaction or the transformation is a local one. Using this property, we find that a seesaw model originally with three generations of left- and right-handed neutrinos, with the left-handed neutrinos unaffected but the right-handed neutrinos transformed under the local FL translation, is reduced to an effective theory of minimal seesaw which has only two right-handed neutrinos. The symmetry predicts that one of the light neutrino masses must be zero.