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The gravitational Compton amplitude at third post-Minkowskian order

N. Emil J. Bjerrum-Bohr, Gang Chen, Carl Jordan Eriksen, Nabha Shah

TL;DR

This work computes the classical gravitational Compton amplitude for a graviton scattering off a non-spinning massive body up to $3$PM using curved-space worldline effective field theory. The method expands around a Schwarzschild–Tangherlini background, builds the $3$PM integrand from recoil and metric-insertion diagrams, and solves master integrals via a canonical differential-equation framework to obtain the IR-exponentiated and finite parts. The authors verify infrared factorization, check against known results, and compare with black hole perturbation theory, finding exact agreement with BHPT at $2$PM and only partial agreement at $3$PM due to subtleties in mapping between frameworks. The results demonstrate the computational power of curved-space worldline EFT for classical gravity amplitudes and illuminate how amplitude methods connect to BH perturbation theory, with implications for scattering-based analyses of massive binaries. Future work will aim to resolve the $3$PM BHPT mismatch and to extend the formalism to higher orders.

Abstract

We compute the classical Compton amplitude for graviton interaction with a non-spinning massive body up to the third post-Minkowskian order. Our novel result utilizes the enhanced computational efficiency provided by worldline effective field theory in a non-trivial background spacetime. Physical constraints, such as infrared factorization, provide a useful cross-check of the result and we also consider its consistency with computations in black hole perturbation theory.

The gravitational Compton amplitude at third post-Minkowskian order

TL;DR

This work computes the classical gravitational Compton amplitude for a graviton scattering off a non-spinning massive body up to PM using curved-space worldline effective field theory. The method expands around a Schwarzschild–Tangherlini background, builds the PM integrand from recoil and metric-insertion diagrams, and solves master integrals via a canonical differential-equation framework to obtain the IR-exponentiated and finite parts. The authors verify infrared factorization, check against known results, and compare with black hole perturbation theory, finding exact agreement with BHPT at PM and only partial agreement at PM due to subtleties in mapping between frameworks. The results demonstrate the computational power of curved-space worldline EFT for classical gravity amplitudes and illuminate how amplitude methods connect to BH perturbation theory, with implications for scattering-based analyses of massive binaries. Future work will aim to resolve the PM BHPT mismatch and to extend the formalism to higher orders.

Abstract

We compute the classical Compton amplitude for graviton interaction with a non-spinning massive body up to the third post-Minkowskian order. Our novel result utilizes the enhanced computational efficiency provided by worldline effective field theory in a non-trivial background spacetime. Physical constraints, such as infrared factorization, provide a useful cross-check of the result and we also consider its consistency with computations in black hole perturbation theory.
Paper Structure (13 sections, 98 equations, 1 figure, 2 tables)

This paper contains 13 sections, 98 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Theoretical setup
  3. Perturbative expansion
  4. Kinematics
  5. Integrand at the third post-Minkowskian order
  6. General structure of the Compton amplitude
  7. Comparison with black hole perturbation theory
  8. Conclusion
  9. Tensor reduction
  10. Differential equations and canonical basis
  11. Integration regions and boundary constants
  12. Integration regions
  13. Boundary constants

Figures (1)

  • Figure 1: Diagrammatic representations of the master integrals. In this type of diagrams, plain solid lines represent a graviton propagator while solid lines cut by a red line represent velocity cut massive propagators (which correspond to a dotted line in the world line quantum field theory diagrams Mogull:2020sak). The dot on the second cut double box signifies a squared propagator.