Structure of Kaluza-Klein Graviton Scattering Amplitudes from Gravitational Equivalence Theorem and Double-Copy

Abstract

We study the structure of scattering amplitudes of the Kaluza-Klein (KK) gravitons and of the gravitational KK Goldstone bosons in the compactified 5d General Relativity (GR). We analyze the geometric "Higgs" mechanism for mass-generation of KK gravitons under compactification with a general $R_{\xi }$ gauge-fixing, which is free from the vDVZ discontinuity. Then, we formulate the Gravitational Equivalence Theorem (GRET) to connect the longitudinal KK graviton amplitudes to the KK Goldstone amplitudes, which is a manifestation of the geometric Higgs mechanism at $S$-matrix level. We directly compute the tree-level KK Goldstone amplitudes which equal the longitudinal KK graviton amplitudes in the high energy limit. We further extend the double-copy method with color-kinematics duality to reconstruct the massive KK longitudinal graviton (Goldstone) amplitudes from the KK longitudinal gauge boson (Goldstone) amplitudes in the compactified 5d Yang-Mills (YM) theory under high energy expansion. From these, we reconstruct the GRET of the KK longitudinal graviton (Goldstone) amplitudes in the 5d GR from the KK longitudinal gauge boson (Goldstone) amplitudes in the 5d YM theory. Using either the GRET or the double-copy reconstruction, we provide a theoretical mechanism showing that the sum of all the energy-power terms [up to $O(E^{10})$] in the high-energy four longitudinal KK graviton amplitudes must cancel down to $O(E^2)$ as enforced by matching the energy-power dependence of the corresponding KK Goldstone amplitudes or by matching that of the double-copy amplitudes from the KK YM theory. With the double-copy approach, we establish a new correspondence between the two energy-cancellations: $E^4\to E^0$ in the 5d KK YM theory and $E^{10}\to E^2$ in the 5d KK GR theory. We further analyze the structure of the residual terms in the GRET and uncover a new energy-cancellation mechanism therein.

90 pages. Final version inclulding the exact KK double-copy of NLO amplitudes. Conclusions unchanged, typos corrected and references added. Its companion Letter paper appeared in arXiv:2207.11214

References in corpus (13)

• The Standard Model Higgs boson as the inflaton
• Resummation of Massive Gravity
• New Relations for Gauge-Theory Amplitudes
• TASI Lectures on Extra Dimensions and Branes
• Higgs Gravitational Interaction, Weak Boson Scattering, and Higgs Inflation in Jordan and Einstein Frames
• Constraints and Generalized Gauge Transformations on Tree-Level Gluon and Graviton Amplitudes
• Extending Higgs Inflation with TeV Scale New Physics
• New Higgs Inflation in a No-Scale Supersymmetric SU(5) GUT
• Supersymmetry in 5d Gravity
• Gauge-Fixing and Residual Symmetries in Gauge/Gravity Theories with Extra Dimensions
• Asymptotically Safe Higgs Inflation
• Structure of Chern-Simons Scattering Amplitudes from Topological Equivalence Theorem and Double-Copy
• Scattering Amplitudes of Kaluza-Klein Strings and Extended Massive Double-Copy

Cited by in corpus (12)

• Compton Black-Hole Scattering for $s\le 5/2$
• Scattering Amplitudes of Kaluza-Klein Strings and Extended Massive Double-Copy
• Scattering Amplitudes of Massive Spin-2 Kaluza-Klein States with Matter
• 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
• Massive Color-Kinematics Duality and Double-Copy for Kaluza-Klein Scattering Amplitudes
• 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
• The seeds of EFT double copy
• Scattering amplitudes in the Randall-Sundrum model with brane-localized curvature terms
• Cotton Double Copy for Gravitational Waves
• Equivalence Theorems and Double-Copy Structure in Scattering Amplitudes of Massive Kaluza-Klein States with Matter Interactions