Abstract
We propose a model that explains the fermion mass hierarchy by the Froggatt-Nielsen mechanism with a discrete {mathrm{mathbb{Z}}}_N^F symmetry. As a concrete model, we study a super-symmetric model with a single flavon coupled to the minimal supersymmetric Standard Model. Flavon develops a TeV scale vacuum expectation value for realizing flavor hierarchy, an appropriate μ-term and the electroweak scale, hence the model has a low cutoff scale. We demonstrate how the flavon is successfully stabilized together with the Higgs bosons in the model. The discrete flavor symmetry {mathrm{mathbb{Z}}}_N^F controls not only the Standard Model fermion masses, but also the Higgs potential and a mass of the Higgsino which is a good candidate for dark matter. The hierarchy in the Higgs-flavon sector is determined in order to make the model anomaly-free and realize a stable electroweak vacuum. We show that this model can explain the fermion mass hierarchy, realistic Higgs-flavon potential and thermally produced dark matter at the same time. We discuss flavor violating processes induced by the light flavon which would be detected in future experiments.
Highlights
Vacuum expectation value (VEV) of flavon to a cutoff scale of a model: a source for the fermion mass hierarchy is given by
We propose a model that explains the fermion mass hierarchy by the FroggattNielsen mechanism with a discrete ZFN symmetry
We study a supersymmetric model with a single flavon coupled to the minimal supersymmetric Standard Model
Summary
+ Wfermion, 7The FN mechanism via an inverse ratio Λ/ S is recently proposed [63, 64]. The scalar potential of the flavon and the neutral Higgs (against U(1)em) is given by. Where Hu0, Hd0 are neutral components of the Higgs doublets Hu, Hd, respectively. Mass eigenvalues for the CP-even and CP-odd flavons are given by m2hs = 2(N − 1)(N − 2) cN N−3vs 2 + AS(N − 2) N−3vs + O vH2 , m2as = − N AS N−3vs + O vH2. The soft mass terms are eliminated by the vacuum condition. In this limit, the minimization conditions for the doublet Higgs bosons are similar to that for the MSSM, m2Z. The full Higgs mass matrices and the vacuum conditions are shown in appendix A. is approximately a mass of the flavino. The charged Higgsino mass is given by μeff
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