Spin-2 Kaluza-Klein mode scattering in models with a massive radion

We calculate tree-level scattering amplitudes of massive spin-2 Kaluza-Klein (KK) particles in models of stabilized compact extradimensional theories. Naïvely introducing a mass for the radion in an extra-dimensional model without accounting for the dynamics responsible for stabilizing the extra dimension upsets the cancellations relating the masses and couplings of the spin-2 modes, resulting in KK scattering amplitudes which grow like $E^4$ instead of $E^2$. We therefore investigate scattering of the Kaluza-Klein states in theories incorporating the Goldberger-Wise mechanism to stabilize the size of the extra dimension. We demonstrate that the cancellations occur only when one includes not only the massive radion, but also the massive spin-0 modes arising from the Goldberger-Wise scalar. We compute the revised sum rules which are satisfied in a stabilized model to ensure a consistent high-energy scattering amplitude. We introduce a simple model of a stabilized extra dimension which is a small deformation of a flat (toroidal) five-dimensional model, and demonstrate the cancellations in computations performed to leading nontrivial order in the deformation. These results are the first complete KK scattering computation in an extra-dimensional model with a stabilized extra dimension, with implications for the theory and phenomenology of these models.

Figure 1

Feynman diagrams contributing to $n,n\to n,n$ massive spin-2 KK boson scattering. In a model incorporating the GW mechanism, the intermediate states $x$ include the radion, the graviton, massive spin-2 KK bosons, and GW scalars of various levels.