Effects of localized μ-terms at the fixed points in magnetized orbifold models

Hiroyuki Abe,Makoto Ishida,Yoshiyuki Tatsuta

doi:10.1016/j.nuclphysb.2019.114732

Hiroyuki Abe, Makoto Ishida + Show 1 more

Open Access

https://doi.org/10.1016/j.nuclphysb.2019.114732

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Abstract

We consider magnetized orbifolds, where the supersymmetric mass term for a pair of up- and down-type Higgs (super)fields, called μ-term, is localized at the orbifold fixed points, and study the effects on the zero-mode spectra. The zero-mode degeneracy to be identified as the generation in four-dimensional (4D) effective theories is determined by the magnetic fluxes. It is known that multiple Higgs zero-modes appear in general in magnetized orbifold models. We derive the analytic form of the μ-term matrix in the 4D effective theory generated by the localized sources on T2/Z2 orbifold fixed points, and find that this matrix can lead to a distinctive pattern of the eigenvalues that yields hierarchical μ-terms for the multiple Higgs fields. The lightest ones can be exponentially suppressed due to the localized wavefunctions of zero-modes determined by the fluxes, while the others are of the order of the compactification scale, which can provide a dynamical origin of the electroweak scale as well as a simultaneous decoupling of extra Higgs fields. We also show that a certain linear combination of the lightest Higgs fields could generate the observed mass ratios of down-type quarks through their Yukawa couplings determined by the wavefunctions.

Highlights

Higgs sector of the minimal supersymmetric standard model (MSSM) consists of two Higgs doublets hu and hd, those form chiral multiplets under the supersymmetry and described by chiral superfields Hu and Hd, respectively
It is known that the mass parameter μ should be of O(102) GeV to reproduce the correct electroweak scale required for explaining the observed masses of electroweak gauge bosons, otherwise a fine-tuning is required between the supersymmetric mass parameter μ and certain supersymmetry breaking mass parameters
There are fixed points in extradimensional space and symmetries such as gauge symmetries and/or supersymmetry are partially broken at these points

Summary

Review of magnetized orbifold models

We review extra-dimensional models with magnetic fluxes on a torus or a toroidal orbifold based on Refs. [2, 5]. We review extra-dimensional models with magnetic fluxes on a torus or a toroidal orbifold based on Refs. (For M < 0, there is no normalizable solution for ψ+, and |M|-degenerated chiral zero-modes ψ− appear.) We can interpret it as a generation structure of the chiral fermion in 4D effective theories, which can be the origin of, e.g., three families of quarks and leptons in the standard model with a suitable choice of fluxes. Given the wavefunctions for spinor and scalar zero-modes on T 2 in the form of Eq (2.6), Yukawa coupling constants in the 4D effective theory can be expressed analytically as [2]. We have to be careful of this property when we construct models

Deformation of Higgs zero-modes by localized μ-terms

Effects of KK excitation modes

Conclusion