On higher-derivative effects on the gravitational potential and particle bending

TL;DR

The paper investigates how higher-derivative gravity terms, specifically $R^3$-type invariants and a dilaton-related $\Phi R^2$ coupling from the bosonic string, modify the gravitational potential and the bending of massless particles. Employing modern on-shell unitarity methods, it separates classical and quantum corrections from one-loop amplitudes for scattering of scalars and for scattering of massless particles off a heavy scalar, revealing a universal classical bending and, intriguingly, a universal first quantum correction across spins in the $R^3$ case. It also computes string-inspired corrections, showing the dilaton-driven $\Phi R^2$ term dominates the graviton bending in that sector and can be significantly larger than the $R^3$ contributions. The results illuminate how higher-derivative operators alter low-energy gravity and offer precise, spin-agnostic predictions for bending angles, with potential implications for effective field theory gravity and string-inspired phenomenology.

Abstract

Using modern amplitude techniques we compute the leading classical and quantum corrections to the classical gravitational potential between two massive scalars induced by adding an $R^3$ term to Einstein gravity. We then study the scattering of massless scalars, photons and gravitons off a heavy scalar in the presence of the same $R^3$ deformation, and determine the bending angle in the three cases from the non-analytic component of the scattering amplitude. Similarly to the Einstein-Hilbert case, we find that the classical contribution to the bending angle is universal, but unlike that case, universality is preserved also by the first quantum correction. Finally we extend our analysis to include a deformation of the form $ΦR^2$, where $Φ$ is the dilaton, which arises in the low-energy effective action of the bosonic string in addition to the $R^3$ term, and compute its effect on the graviton bending.

Figures (4)

• Figure 1: The two cut diagrams contributing to the leading $R^3$ correction to the gravitational scattering of two massive scalars. The two gravitons crossing the cut have both either positive or negative helicity and we have indicated this next to the dashed lines.
• Figure 2: The cut diagram contributing to the leading $R^3$ correction to gravitational scattering of a photon (wavy lines) off a massive scalar (double lines).
• Figure 3: The cut diagram contributing to the leading $R^3$ correction to gravitational scattering of a graviton (double wavy lines) off a massive scalar (double lines).
• Figure 4: The cut diagram contributing to the leading $(\Phi R^2)^2$ correction to gravitational scattering of a graviton (double wavy lines) off a massive scalar (double lines).