Graviton bending in quantum gravity from one-loop amplitudes

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-1/2 and spin-1 particles [N. E. J. Bjerrum-Bohr, J. F. Donoghue, B. R. Holstein, L. Plante, and P. Vanhove, Phys. Rev. Lett. 114, 061301 (2015); N. E. J. Bjerrum-Bohr, J. F. Donoghue, B. R. Holstein, L. Plante, and P. Vanhove, J. High Energy Phys. 11 (2016) 117; D. Bai and Y. Huang, Phys. Rev. D 95,064045 (2017).], 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.