Tri-Bimaximal Mixing from Twisted Friedberg-Lee Symmetry

TL;DR

This paper explores the twisted Friedberg-Lee symmetry, combining it with mu-tau symmetry, to develop models that naturally produce the tri-bimaximal neutrino mixing pattern.

Contribution

It introduces the concept of twisted FL symmetry and proposes two novel schemes for achieving realistic neutrino masses and tri-bimaximal mixing.

Findings

Two viable models based on twisted FL symmetry are constructed.

The models successfully reproduce the tri-bimaximal mixing pattern.

Breaking terms consistent with the symmetry are incorporated.

Abstract

We investigate the Friedberg-Lee (FL) symmetry and its promotion to include the $\mu - \tau$ symmetry, and call that the twisted FL symmetry.Based on the twisted FL symmetry, two possible schemes are presented toward the realistic neutrino mass spectrum and the tri-bimaximal mixing.In the first scheme, we suggest the semi-uniform translation of the FL symmetry.The second one is based on the $S_3$ permutation family symmetry.The breaking terms, which are twisted FL symmetric, are introduced.Some viable models in each scheme are also presented.