Effects of localized {\mu}-terms at the fixed points in magnetized orbifold models

TL;DR

This paper analyzes how localized {b}-terms at orbifold fixed points influence zero-mode spectra in magnetized orbifold models, leading to hierarchical Higgs masses and potential explanations for the electroweak scale and quark mass ratios.

Contribution

It derives the analytic form of the {b}-term matrix in magnetized orbifolds and shows how it produces hierarchical Higgs masses and realistic quark mass ratios.

Findings

Hierarchical {b}-terms can be generated by localized sources.

Lightest Higgs modes can be exponentially suppressed.

The model explains the electroweak scale and quark mass ratios.

Abstract

We consider magnetized orbifolds, where the supersymmetric mass term for a pair of up- and down-type Higgs (super)fields, called $\mu$-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 $\mu$-term matrix in the 4D effective theory generated by the localized sources on $T^2/Z_2$ orbifold fixed points, and find that this matrix can lead to a distinctive pattern of the eigenvalues that yields hierarchical $\mu$-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.