# Scattering Amplitudes of Massive Spin-2 Kaluza-Klein States Grow Only as ${\cal O}(s)$

## TL;DR

This paper calculates high-energy scattering amplitudes of massive spin-2 Kaluza-Klein states, revealing cancellations that limit growth to linear in energy, impacting the understanding of their theoretical and phenomenological validity.

## Contribution

First complete tree-level calculation showing cancellations in spin-2 KK scattering amplitudes, reducing growth from ${
m O}(s^5)$ to ${
m O}(s)$, with implications for effective field theories.

## Key findings

- Amplitudes grow as ${
m O}(s)$ at high energies.
- Cancellations depend on mass-interaction relationships.
- Results impact the validity of theories involving massive spin-2 KK states.

## Abstract

We present the results of the first complete calculation of the tree-level $2\to 2$ high-energy scattering amplitudes of the longitudinal modes of massive spin-2 Kaluza-Klein states, both in the case where the internal space is a torus and in the Randall-Sundrum model where the internal space has constant negative curvature. While individual contributions to this amplitude grow as ${\cal O}(s^5$), we demonstrate explicitly that intricate cancellations occur between different contributions, reducing the growth to ${\cal O}(s)$, a slower rate of growth than previously argued in the literature. These cancellations require subtle relationships between the masses of the Kaluza-Klein states and their interactions, and reflect the underlying higher-dimensional diffeomorphism invariance. Our results provide fresh perspective on the range of validity of (effective) field theories involving massive spin-2 KK particles, with significant implications for the theory and phenomenology of these states.