Tree-level unitarity in Gauge-Higgs Unification

TL;DR

This paper estimates the energy scale at which tree-level unitarity breaks down in the Gauge-Higgs unification model, highlighting differences between warped and flat spacetimes and the impact of the Wilson line phase.

Contribution

It provides a numerical estimation of the unitarity violation scale in the SO(5)×U(1)_X gauge-Higgs unification model considering both elastic and inelastic scattering effects.

Findings

Unitarity violation scale is about 1.3 times the Kaluza-Klein mass in warped spacetime.

Unitarity violation scale is about 140 times the Kaluza-Klein mass in flat spacetime.

Unitarity is violated around 1 TeV for certain Wilson line phases due to vanishing WWH coupling.

Abstract

We numerically estimate a scale $\Lambda_{uni}$ at which tree-level unitarity is violated in the $SO(5)\times U(1)_X$ gauge-Higgs unification model by evaluating amplitudes for scattering of the longitudinal W bosons. The scattering amplitudes take larger values in the warped spacetime than in the flat spacetime, and take maximal values when $\theta_H=\pi/2$, where $\theta_H$ is the Wilson line phase along the extra dimension. We take into account not only the elastic scattering but also possible inelastic scatterings in order to estimate $\Lambda_{\rm uni}$. We found that $\Lambda_{\rm uni}\simeq 1.3m_{KK}$ in the warped spacetime, and $\Lambda_{\rm uni}\simeq 140m_{KK}$ in the flat spacetime, where $m_{KK}$ is the Kaluza-Klein mass scale. The tree-level unitarity is violated at $O(1TeV)$ for $\theta_H=\pi/2$ in the former case due to the vanishing WWH coupling.