Tree-level unitarity in Gauge-Higgs Unification

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 ${\Lambda }_{\mathrm{uni}}$. We found that ${\Lambda }_{\mathrm{uni}}\simeq 1.3m_{KK}$ in the warped spacetime, and ${\Lambda }_{\mathrm{uni}}\simeq 140m_{KK}$ 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.

Comments: 37 pages, 9 figures, some comments added