Equivalence Theorems and Double-Copy Structure in Scattering Amplitudes of Massive Kaluza-Klein States with Matter Interactions

Abstract

We investigate the scattering amplitudes of massive Kaluza-Klein (KK) states in compactified five-dimensional warped gauge and gravity theories. Focusing on tree-level $2\to 2$ processes, we analyze the leading-order amplitudes involving bulk KK matter fields and KK gauge/gravitational Goldstone bosons. By imposing the gauge theory equivalence theorem (GAET) and the gravitational equivalence theorem (GRET) within warped KK theories, we systematically reconstruct the leading-order amplitudes for physical KK gauge bosons and gravitons, thereby circumventing the intricate energy cancellations inherent in physical amplitudes. Within this framework, the correspondence between GAET and GRET arises as a direct manifestation of the leading-order double-copy relation in the high-energy expansion. This connection provides a foundation for extending the BCJ double-copy construction to four-point amplitudes involving bulk KK matter fields, and further generalizes to arbitrary $N$-point cases, enabling a systematic derivation of the corresponding gravitational amplitudes with consistent incorporation of KK matter fields at leading order.

37 pages. Refined version to match JHEP published version; multiple typos corrected and references updated

References in corpus (29)

• A Large Mass Hierarchy from a Small Extra Dimension
• An Alternative to Compactification
• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• New Relations for Gauge-Theory Amplitudes
• New Recursion Relations for Tree Amplitudes of Gluons
• Bulk Fields and Supersymmetry in a Slice of AdS
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Unitarity of Compactified Five Dimensional Yang-Mills Theory
• Pure Gravities via Color-Kinematics Duality for Fundamental Matter
• Color-Kinematics Duality for QCD Amplitudes
• Double copy for massive quantum particles with spin
• Chiral fermions, orbifolds, scalars and fat branes
• Electroweak Symmetry Breaking and Extra Dimensions
• Constraints on a Massive Double-Copy and Applications to Massive Gravity
• The Phenomenology of Universal Extra Dimensions at Hadron Colliders
• Supersymmetry in 5d Gravity
• Higgsless Deconstruction Without Boundary Condition
• Kaluza-Klein from Colour-Kinematics Duality for Massive Fields
• Gauge-Fixing and Residual Symmetries in Gauge/Gravity Theories with Extra Dimensions
• Structure of Kaluza-Klein Graviton Scattering Amplitudes from Gravitational Equivalence Theorem and Double-Copy
• Structure of Chern-Simons Scattering Amplitudes from Topological Equivalence Theorem and Double-Copy
• Scattering Amplitudes of Kaluza-Klein Strings and Extended Massive Double-Copy
• Gravitational Equivalence Theorem and Double-Copy for Kaluza-Klein Graviton Scattering Amplitudes
• Symmetries, Spin-2 Scattering Amplitudes, and Equivalence theorems in Warped Five-Dimensional Gravitational Theories
• KLT Factorization of Winding String Amplitudes
• Massive Color-Kinematics Duality and Double-Copy for Kaluza-Klein Scattering Amplitudes
• More on divergences in brane world models
• Topological Equivalence Theorem and Double-Copy for Chern-Simons Scattering Amplitudes
• Structure of Massive Gauge/Gravity Scattering Amplitudes, Equivalence Theorems, and Extended Double-Copy with Compactified Warped Space