Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Classical Gravitational Scattering at ${\cal O}(G^3)$ from Feynman Diagrams

Clifford Cheung, Mikhail P. Solon

TL;DR

The paper computes the classical gravitational scattering amplitude at $O(G^3)$ using two-loop Feynman diagrams. It leverages the test-particle limit and multiple gauges to ensure gauge invariance and cross-checks the calculation against the known $3PM$ result. The result exactly reproduces the $3PM$ amplitude and the same velocity resummation up to $6PN$, reinforcing the consistency of amplitudes-based approaches with traditional PN/PM methods. This work demonstrates the ongoing viability of standard Feynman-diagram methods and EFT techniques for classical gravity and supports extending these methods to higher orders.

Abstract

We perform a Feynman diagram calculation of the two-loop scattering amplitude for gravitationally interacting massive particles in the classical limit. Conveniently, we are able to sidestep the most taxing diagrams by exploiting the test-particle limit in which the system is fully characterized by a particle propagating in a Schwarzschild spacetime. We assume a general choice of graviton field basis and gauge fixing that contains as a subset the well-known deDonder gauge and its various cousins. As a highly nontrivial consistency check, all gauge parameters evaporate from the final answer. Moreover, our result exactly matches that of Bern et al., here verified up to sixth post-Newtonian order while also reproducing the same unique velocity resummation at third post-Minkowksian order.

Classical Gravitational Scattering at ${\cal O}(G^3)$ from Feynman Diagrams

TL;DR

The paper computes the classical gravitational scattering amplitude at using two-loop Feynman diagrams. It leverages the test-particle limit and multiple gauges to ensure gauge invariance and cross-checks the calculation against the known result. The result exactly reproduces the amplitude and the same velocity resummation up to , reinforcing the consistency of amplitudes-based approaches with traditional PN/PM methods. This work demonstrates the ongoing viability of standard Feynman-diagram methods and EFT techniques for classical gravity and supports extending these methods to higher orders.

Abstract

We perform a Feynman diagram calculation of the two-loop scattering amplitude for gravitationally interacting massive particles in the classical limit. Conveniently, we are able to sidestep the most taxing diagrams by exploiting the test-particle limit in which the system is fully characterized by a particle propagating in a Schwarzschild spacetime. We assume a general choice of graviton field basis and gauge fixing that contains as a subset the well-known deDonder gauge and its various cousins. As a highly nontrivial consistency check, all gauge parameters evaporate from the final answer. Moreover, our result exactly matches that of Bern et al., here verified up to sixth post-Newtonian order while also reproducing the same unique velocity resummation at third post-Minkowksian order.

Paper Structure

This paper contains 7 sections, 15 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Setup
  3. Action
  4. Classical Limit
  5. Test-Particle Limit
  6. Feynman Diagrams
  7. Results and Outlook

Figures (2)

  • Figure 1: Sample Feynman diagrams corresponding to the test-particle limit at 2PM, 3PM, and 4PM. Thick horizontal lines and thin lines respectively denote massive scalars and exchanged gravitons. Other variants include nonplanar topologies and those involving the seagull vertex.
  • Figure 2: Two-loop Feynman diagrams for classical scattering. Not shown here are diagrams such as those in Fig. \ref{['fig:testparticle']}, which are trivially fixed by the test-particle limit, as well as "twisted" graphs obtained by swapping the incoming and outgoing legs for particle 1, or equivalently, for particle 2. The peculiar labeling is meant to align with the topologies defined in Fig. 14 of 3PM, and the primed labels denote graphs in which an exchanged graviton has been pinched.