Spin-2 KK Mode Scattering in Models with a Massive Radion

TL;DR

This paper calculates scattering amplitudes of massive spin-2 Kaluza-Klein particles in stabilized extra-dimensional models, showing that proper inclusion of all relevant modes ensures cancellations that prevent unphysical growth of amplitudes at high energies.

Contribution

It provides the first complete calculation of KK scattering in a stabilized extra-dimensional model, highlighting the importance of including all relevant scalar modes for consistency.

Findings

Cancellations occur only when all scalar modes are included.

Scattering amplitudes grow as E^2 when models are properly stabilized.

Introduces a simple stabilized model demonstrating these effects.

Abstract

We calculate tree-level scattering amplitudes of massive spin-2 KK particles in models of stabilized compact extra-dimensional theories. Naively 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.