Lepton Private Higgs and the discrete group \Sigma(81)

TL;DR

This paper investigates a specific parameter space in the Private Higgs model using the discrete group (81), proposing explanations for neutrino mass patterns and the muon magnetic moment anomaly, and predicting new Higgs and neutrino states.

Contribution

It introduces a novel application of the (81) group to the Private Higgs model, linking neutrino masses and muon anomaly explanations with new particle predictions.

Findings

Predicts three nearly degenerate Higgs doublets (~500 GeV to 1 TeV)

Predicts three nearly degenerate TeV-scale neutrinos

Provides a group-theoretic framework for (81) in particle physics

Abstract

We use the discrete group \Sigma(81) = (Z_3 x Z_3 x Z_3)\rtimes Z_3 to explore a particular region of parameter space in the Private Higgs model. In doing so we suggest a relation among the off-diagonal entries of the neutrino mass matrix and a possible explanation for the muon magnetic moment anomaly, a_\mu^{exp}-a_\mu^{SM} ~ 10^{-9}. We predict three new nearly degenerate Higgs doublets with masses of order ~ 500 GeV to ~ 1 TeV, and three nearly degenerate SM-singlet TeV-scale neutrinos. The largest scale in the model is ~ 10 TeV, so there is no severe hierarchy problem. The appendix is devoted to the group theory of \Sigma(81).