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.
Highlights
Examining the possibility of extra spatial dimensions has a long history [1,2,3], and has been of particular interest for constructing possible solutions to the hierarchy problem [4,5,6,7,8]
We compute the tree-level elastic 2-to-2 scattering amplitude of helicity-0, KK level-n, massive spin-2 KK modes in a Goldberger and Wise (GW) model with a stabilized extra dimension; we identify generalized sum rules controlling the growth of the scattering amplitude; and we show that the cancellations between the different contributions to the scattering amplitude persist once one includes the new contributions to massive spin-2 KK mode scattering from the GW sector
Having identified the generalized sum rules which must be satisfied, we introduce a simple model of a stabilized extra dimension in which we can explicitly demonstrate these cancellations
Summary
Examining the possibility of extra spatial dimensions has a long history [1,2,3], and has been of particular interest for constructing possible solutions to the hierarchy problem [4,5,6,7,8]. We compute the tree-level elastic 2-to-2 scattering amplitude of helicity-0, KK level-n, massive spin-2 KK modes in a GW model with a stabilized extra dimension; we identify generalized sum rules controlling the growth of the scattering amplitude; and we show that the cancellations between the different contributions to the scattering amplitude persist once one includes the new contributions to massive spin-2 KK mode scattering from the GW sector. The flat stabilized model provides a simple explicit realization of the GW mechanism and allows us to illustrate how the sum rules maintain their validity as the stabilized geometry becomes relevant These results are the first complete scattering computation in an extra-dimensional model with a stabilized extra dimension.
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