Spin-2 Kaluza-Klein Scattering in a Stabilized Warped Background

TL;DR

This paper shows that the high-energy growth of scattering amplitudes involving massive spin-2 Kaluza-Klein modes in a stabilized warped background cancels due to sum rules, extending previous results to warped geometries relevant for hierarchy models.

Contribution

It generalizes scalar sum rules ensuring amplitude cancellations to warped backgrounds in five-dimensional gravity models, with analytic proofs and detailed derivations.

Findings

High-energy amplitude growth cancels for KK spin-2 modes.

Sum rules from scalar exchanges persist in warped geometries.

Analytic proof of scalar sum rule dependence on background geometry.

Abstract

Scattering amplitudes involving massive spin-2 particles typically grow rapidly with energy. In this paper we demonstrate that the anomalous high-energy growth of the scattering amplitudes cancel for the massive spin-2 Kaluza-Klein modes arising from compactified five-dimensional gravity in a stabilized warped geometry. Generalizing previous work, we show that the two sum rules which enforce the cancellations between the contributions to the scattering amplitudes coming from the exchange of the (massive) radion and those from the exchange of the tower of Goldberger-Wise scalar states (admixtures of the original gravitational and scalar fields of the theory) still persist in the case of the warping which would be required to produce the hierarchy between the weak and Planck scales in a Randall-Sundrum model. We provide an analytic proof of one combination of these generalized scalar sum rules, and show how the sum rule depends on the Einstein equations determining the background geometry and the mode-equations and normalization of the tower of physical scalar states. Finally, we provide a consistent and self-contained derivation of the equations governing the physical scalar modes and we list, in appendices, the full set of sum rules ensuring proper high-energy growth of all $2 \to 2$ massive spin-2 scattering amplitudes.