Abstract
We numerically estimate a scale Λuni at which tree-level unitarity is violated in the SO(5) × 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 θ H = π/2, where θ 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 Λuni. We found that Λuni ≃ 1.3m KK in the warped spacetime, and Λuni ≃ 140m KK in the flat spacetime, where m KK is the Kaluza-Klein mass scale. The tree-level unitarity is violated at \( \mathcal{O}\left( {1\,{\text{TeV}}} \right) \) for θ H = π/2 in the former case due to the vanishing WWH coupling.
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