Bending of Light in Quantum Gravity

We consider the scattering of lightlike matter in the presence of a heavy scalar object (such as the Sun or a Schwarzschild black hole). By treating general relativity as an effective field theory we directly compute the nonanalytic components of the one-loop gravitational amplitude for the scattering of massless scalars or photons from an external massive scalar field. These results allow a semiclassical computation of the bending angle for light rays grazing the Sun, including long-range $\hslash$ contributions. We discuss implications of this computation, in particular, the violation of some classical formulations of the equivalence principle.

Figure 1

The two gravitons cut for the amplitude between a massless particle (dashed line) and the massive scalar (solid line). The gray blobs are tree-level gravitational Compton amplitudes.