Higgs potential in gauge-Higgs unification with a flat extra dimension

TL;DR

This paper investigates the Higgs potential in gauge-Higgs unification models with flat extra dimensions, showing that deviations from the Standard Model are small unless models are significantly extended.

Contribution

It provides a detailed analysis of the Higgs potential in flat extra dimension gauge-Higgs unification models, including Lorentz violation effects and potential deviations at colliders.

Findings

Deviation of triple Higgs coupling less than 10% for compactification scale > 5 TeV

Higgs potential shape approaches minimal Higgs potential as scale increases

Observable deviations at future colliders require model extensions

Abstract

We analyze the structure of the Higgs potential in gauge-Higgs unification with a flat extra dimension. As a concrete model, we first consider the cases where the Standard Model Higgs doublet is embedded into a higher-dimensional $SU(3)_{w}^{}$ gauge multiplet with five-dimensional Lorentz symmetry relaxed. In this $SU(3)_{w}^{}$ model with Lorentz violation, the deviation of the resulting triple Higgs boson coupling from its SM prediction is shown to be less than $10\%$ when the compactification scale is larger than the experimental lower bound, which is around 5 TeV. Next, we examine the Higgs potential in other similar gauge-Higgs unification models with a flat extra dimension. It is pointed out that even in such models the shape of the Higgs potential around the vacuum quickly approaches that of the minimal Higgs potential with one Higgs doublet as the compactification scale of the extra dimension increases. An observable deviation of the triple Higgs boson coupling at planned lepton colliders will necessitate significant extensions of such gauge-Higgs unification models.