More on the Bending of Light in Quantum Gravity

TL;DR

The gravity-focused paper investigates one-loop quantum gravity corrections to light bending from scattering of massless scalars and photons by a massive scalar. It decomposes quantum corrections into graviton double-cut, massless-scalar double-cut, and photon double-cut contributions, cross-checking graviton double-cut results with prior work that used on-shell unitarity and double-copy methods. It finds that while graviton double-cut results agree with previous analyses, the massless-scalar and photon double-cut contributions yield non-vanishing quantum effects on scattering amplitudes and light bending, yet preserve the overall amplitude structure and the proposed quantum discrepancy of the equivalence principle. These findings strengthen confidence in the previous framework while highlighting additional quantum contributions and their consistency with overarching gravitational amplitude structure.

Abstract

We reconsider the long-range effects of the scattering of massless scalars and photons from a massive scalar object in quantum gravity. At the one-loop level, the relevant quantum mechanical corrections could be sorted into the graviton double-cut contributions, massless-scalar double-cut contributions and photon double-cut contributions. In arXiv:1410.7590 and 1609.07477 N.E.J. Bjerrum-Bohr et al. have considered explicitly the implications of the graviton double-cut contributions on the gravitational bending of light and some classical formulations of the equivalence principle, using the modern double-copy constructions and on-shell unitarity techniques. In this article, instead we consider all three contributions and redo the analysis using the traditional Feynman diagrammatic approach. Our results on the graviton double-cut contributions agree with the aforementioned references, which acts as a nontrivial check of previous computations. Furthermore, it turns out that the massless-scalar double-cut contributions and the photon double-cut contributions do leave non-vanishing quantum effects on the scattering amplitudes and the gravitational bending of light. Yet, we find that the general structure of the gravitational amplitudes and the quantum discrepancy of the equivalence principle suggested in the aforementioned references remain intact.