Sum Rules for Massive Spin-2 Kaluza-Klein Elastic Scattering Amplitudes

Abstract

It has recently been shown explicitly that the high-energy scattering amplitude of the longitudinal modes of massive spin-2 Kaluza Klein states in compactified 5-dimensional gravity, which would naively grow like O(s^5), grow only like O(s). Since the individual contributions to these amplitudes do grow like O(s^5), the required cancellations between these individual contributions result from intricate relationships between the masses of these states and their couplings. Here we report the explicit form of these sum-rule relationships which ensure the necessary cancellations for elastic scattering of spin-2 Kaluza Klein states in a Randall-Sundrum model. We consider an Anti-de-Sitter space of arbitrary curvature, including the special case of a toroidal compactification in which the curvature vanishes. The sum rules demonstrate that the cancellations at O(s^5) and O(s^4) are generic for a compact extra dimension, and arise from the Sturm-Liouville structure of the eigenmode system in the internal space. Separately, the sum rules at O(s^3) and O(s^2) illustrate the essential role of the radion mode of the extra-dimensional metric, which is the dynamical mode related to the size of the internal space.

Minor revisions added in response to referee

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• Graviton-photon production with a massive spin-2 particle
• Spin-2 KK Mode Scattering in Models with a Massive Radion
• Bootstrap Bounds on Closed Einstein Manifolds
• Unitarity in KK-graviton production: A case study in warped extra-dimensions
• Scattering Amplitudes of Massive Spin-2 Kaluza-Klein States with Matter
• Symmetries, Spin-2 Scattering Amplitudes, and Equivalence theorems in Warped Five-Dimensional Gravitational Theories
• Limits on Kaluza-Klein Portal Dark Matter Models
• Gravity-Matter Sum Rules in models with a single extra-dimension
• 5-Dimensional Chern-Simons Gauge Theory on an Interval: Massive Spin-2 Theory from Symmetry Breaking via Boundary Conditions
• Identifying the Quantum Properties of Hadronic Resonances using Machine Learning
• Scattering amplitudes in the Randall-Sundrum model with brane-localized curvature terms