Scattering Amplitudes of Massive Spin-2 Kaluza-Klein States with Matter

Abstract

We perform a comprehensive analysis of the scattering of matter and gravitational Kaluza-Klein (KK) modes in five-dimensional gravity theories. We consider matter localized on a brane as well as in the bulk of the extra dimension for scalars, fermions and vectors respectively, and consider an arbitrary warped background. While naive power-counting suggests that there are amplitudes which grow as fast as $\mathcal{O}(s^3)$ [where $s$ is the center-of-mass scattering energy-squared], we demonstrate that cancellations between the various contributions result in a total amplitude which grows no faster than $\mathcal{O}(s)$. Extending previous work on the self-interactions of the gravitational KK modes, we show that these cancellations occur due to sum-rule relations between the couplings and the masses of the modes that can be proven from the properties of the mode equations describing the gravity and matter wavefunctions. We demonstrate that these properties are tied to the underlying diffeomorphism invariance of the five-dimensional theory. We discuss how our results generalize when the size of the extra dimension is stabilized via the Goldberger-Wise mechanism. Our conclusions are of particular relevance for freeze-out and freeze-in relic abundance calculations for dark matter models including a spin-2 portal arising from an underlying five-dimensional theory.

34 pages, 3 figures. Footnote added on page 2. Minor corrections, references updated, version published in PRD

References in corpus (13)

• A Confining Strong First-Order Electroweak Phase Transition
• A Holographic Perspective on the Axion Quality Problem
• Supersymmetry in 5d Gravity
• Gauge-Fixing and Residual Symmetries in Gauge/Gravity Theories with Extra Dimensions
• Sum Rules for Massive Spin-2 Kaluza-Klein Elastic Scattering Amplitudes
• Structure of Kaluza-Klein Graviton Scattering Amplitudes from Gravitational Equivalence Theorem and Double-Copy
• Graviton-photon production with a massive spin-2 particle
• Massive Gravitons as Feebly Interacting Dark Matter Candidates
• Warm dark matter from a gravitational freeze-in in extra dimensions
• Spin-2 KK Mode Scattering in Models with a Massive Radion
• FIMP Dark Matter in Clockwork/Linear Dilaton Extra-Dimensions
• Unitarity in KK-graviton production: A case study in warped extra-dimensions
• Massive Color-Kinematics Duality and Double-Copy for Kaluza-Klein Scattering Amplitudes

Cited by in corpus (4)

• 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
• Scattering amplitudes in the Randall-Sundrum model with brane-localized curvature terms