Light-like Scattering in Quantum Gravity

TL;DR

The paper develops an EFT approach to quantum gravity and computes one-loop, light-like scattering of massless fields from a heavy scalar source using on-shell amplitude techniques, revealing both universal classical post-Newtonian corrections and quantum $\hbar$-dependent terms. By combining unitarity-based loop construction with BCJ/KLT-type relations, the authors derive explicit integral coefficients for scalars, photons, and fermions and confirm that the leading long-range behavior reproduces GR predictions. The bending of light is analyzed via the eikonal method and geometrical optics, showing consistent classical results and identifying a quantum correction term that scales as $\hbar$ and depends on the external particle type. The work highlights the utility of EFT+amplitude methods for gravity, confirms the universality of classical effects, and clarifies the structure and potential observability of quantum gravitational corrections at low energies.

Abstract

We consider scattering in quantum gravity and derive long-range classical and quantum contributions to the scattering of light-like bosons and fermions (spin-0, spin-1/2, spin-1) from an external massive scalar field, such as the Sun or a black hole. This is achieved by treating general relativity as an effective field theory and identifying the non-analytic pieces of the one-loop gravitational scattering amplitude. It is emphasized throughout the paper how modern amplitude techniques, involving spinor-helicity variables, unitarity, and squaring relations in gravity enable much simplified computations. We directly verify, as predicted by general relativity, that all classical effects in our computation are universal (in the context of matter type and statistics). Using an eikonal procedure we confirm the post-Newtonian general relativity correction for light-like bending around large stellar objects. We also comment on treating effects from quantum hbar dependent terms using the same eikonal method.

Figures (4)

• Figure 1: The one-loop scattering of one massless scalars (dotted line) and one massive scalars (solid line) mediated by a graviton (curly line). The discontinuity cut is represented by the red line.
• Figure 2: The monodromy BCJ relations in the cut (in red) that link the one-loop integral coefficients.
• Figure 3: Gravitional Compton scattering given by the tree-level scattering a massless particle (wavy line) on graviton (curly line) with only gravitational interactions.
• Figure 4: One graviton exchange between a massless fields and a massive scalar.