Generalization of Friedberg-Lee Symmetry

TL;DR

This paper explores the origin and implications of Friedberg-Lee symmetry in neutrino physics, proposing a generalized form that can be spontaneously broken and lead to realistic neutrino masses and mixings, including testable TeV scale see-saw models.

Contribution

It introduces a generalized Friedberg-Lee symmetry incorporating scalar fields, links it to realistic neutrino mass models, and connects it with $SO(3)\times U(1)$ flavor symmetry breaking.

Findings

Generalized Friedberg-Lee symmetry allows realistic neutrino masses.

TeV scale see-saw mechanism can be tested experimentally.

Neutrino mass matrices resemble those with Friedberg-Lee symmetry after flavor symmetry breaking.

Abstract

We study the possible origin of Friedberg-Lee symmetry. First, we propose the generalized Friedberg-Lee symmetry in the potential by including the scalar fields in the field transformations, which can be broken down to the FL symmetry spontaneously. We show that the generalized Friedberg-Lee symmetry allows a typical form of Yukawa couplings, and the realistic neutrino masses and mixings can be generated via see-saw mechanism. If the right-handed neutrinos transform non-trivially under the generalized Friedberg-Lee symmetry, we can have the testable TeV scale see-saw mechanism. Second, we present two models with the $SO(3)\times U(1)$ global flavour symmetry in the lepton sector. After the flavour symmetry breaking, we can obtain the charged lepton masses, and explain the neutrino masses and mixings via see-saw mechanism. Interestingly, the complete neutrino mass matrices are similar to those of the above models with generalized Friedberg-Lee symmetry. So the Friedberg-Lee symmetry is the residual symmetry in the neutrino mass matrix after the $SO(3)\times U(1)$ flavour symmetry breaking.