Scattering amplitudes of massive spin-2 Kaluza-Klein states grow only as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="script">O</mml:mi><mml:mo mathvariant="bold" stretchy="false">(</mml:mo><mml:mi>s</mml:mi><mml:mo mathvariant="bold" stretchy="false">)</mml:mo></mml:mrow></mml:math>
R. Sekhar Chivukula, Dennis Foren, Kirtimaan A. Mohan, Dipan Sengupta, Elizabeth H. Simmons
Abstract
We present the results of the first complete calculation of the tree-level $2\ensuremath{\rightarrow}2$ high-energy scattering amplitudes of the longitudinal modes of massive spin-2 Kaluza-Klein (KK) 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 $\mathcal{O}({s}^{5})$, we demonstrate explicitly that intricate cancellations occur between different contributions, reducing the growth to $\mathcal{O}(s)$, 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.