Equivalence theorems and double-copy structure in scattering amplitudes of massive Kaluza-Klein states with matter interactions

A bstract 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 → 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.