Graviton-Photon Scattering

TL;DR

The work extends a gravity–gauge amplitude factorization to charged spin-1 targets, showing that gravitational tree amplitudes can be written as the product of corresponding Abelian QED amplitudes times a universal kinematic factor ${H}$, thereby enabling straightforward calculations of graviton photoproduction and gravitational Compton scattering using familiar electromagnetic methods. It demonstrates a universal, spin-insensitive low-energy behavior across these processes and clarifies subtleties in the massless limit for photon–graviton scattering, including the necessity to exclude the longitudinal mode in gauge-invariant treatments. The forward cross sections exhibit distinct, process-dependent divergences reflecting long-range interactions, with connections to classical light bending in a Schwarzschild background. Together, these results unify gravity and electromagnetism at tree level for spin-1 and point toward potential indirect avenues for graviton detection and higher-order extensions.

Abstract

We use the feature that the gravitational Compton scattering amplitude factorizes in terms of Abelian QED amplitudes to evaluate various gravitational Compton processes. We examine both the QED and gravitational Compton scattering from a massive spin-1 system by the use of helicity amplitude methods. In the case of gravitational Compton scattering we show how the massless limit can be used to evaluate the cross section for graviton-photon scattering and discuss the difference between photon interactions and the zero mass spin-1 limit. We show that the forward scattering cross section for graviton photoproduction has a very peculiar behavior, differing from the standard Thomson and Rutherford cross sections for a Coulomb-like potential.

Figures (5)

• Figure 1: Diagrams relevant to Compton scattering.
• Figure 2: (a) The one-graviton and (b) two-graviton emission vertices from either a scalar, spinor or vector particle.
• Figure 3: The three graviton vertex
• Figure 4: Diagrams relevant to graviton photoproduction.
• Figure 5: Diagrams relevant for gravitational Compton scattering.