# Graviton Bending in Quantum Gravity from One-Loop Amplitudes

## TL;DR

This paper investigates quantum corrections to graviton bending angles near massive objects using scattering amplitudes, revealing violations of the equivalence principle at the quantum level and providing a universal formula for the bending angle.

## Contribution

It extends previous work by including gravitons, offers a universal expression for bending angles, and compares effects across different particle spins.

## Key findings

- Quantum corrections differ for particles with different spins.
- A universal formula for bending angles in the low energy limit is derived.
- Quantum effects violate the classical equivalence principle.

## Abstract

We study the bending of gravitons that pass near a massive object like the Sun, using scattering amplitudes in which the Sun is represented by a massive scalar particle. Our results complete previous work on the bending angles of massless spin-0, spin-$\frac{1}{2}$ and spin-1 particles, and provides more evidence for the violation of the equivalence principle at the quantum level, in the sense that the quantum corrections to bending angles for massless particles with different spins are different. We provide a universal expression for the bending angle in terms of coefficients of triangle and bubble integrals in the amplitudes in the low energy limit. We also compare bending angles for scalar, photon and graviton projectiles under different circumstances.