Tri-bimaximal lepton mixing from symmetry only

TL;DR

This paper presents a model for tri-bimaximal lepton mixing using only family symmetries and their soft breaking, avoiding complex mechanisms like vacuum alignment or supersymmetry, and extends the Standard Model with additional neutrinos and Higgs fields.

Contribution

The model uniquely employs only family symmetries and their soft breaking to achieve tri-bimaximal mixing without relying on vacuum alignment or supersymmetry.

Findings

Constructs a lepton mixing model based solely on family symmetries.

Uses the permutation group S_3 and lepton number symmetries as the core symmetry group.

Does not make specific predictions for neutrino masses.

Abstract

We construct a model for tri-bimaximal lepton mixing which employs only family symmetries and their soft breaking; neither vacuum alignment nor supersymmetry, extra dimensions, or non-renormalizable terms are used in our model. It is an extension of the Standard Model making use of the seesaw mechanism with five right-handed neutrino singlets. The scalar sector comprises four Higgs doublets and one complex gauge singlet. The horizontal symmetry of our model is based on the permutation group S_3 of the lepton families together with the three family lepton numbers--united this constitutes a symmetry group Delta(6\infty^2). The model makes no predictions for the neutrino masses.