Tree-level unitarity in Gauge-Higgs Unification

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 θH = π/2, where θH 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 ≃ 1.3mKK in the warped spacetime, and Λuni ≃ 140mKK in the flat spacetime, where mKK is the Kaluza-Klein mass scale. The tree-level unitarity is violated at O(1 TeV) for θH = π/2 in the former case due to the vanishing WWH coupling. e-mail address: [email protected] e-mail address: [email protected] e-mail address: [email protected]