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

## TL;DR

This paper uses amplitude techniques to compute classical and quantum corrections to gravitational interactions caused by higher-derivative terms like R^3 and Phi R^2, affecting potential and bending angles.

## Contribution

It provides the first detailed analysis of how R^3 and Phi R^2 terms modify gravitational potential and particle bending, including quantum effects.

## Key findings

- Classical gravitational potential receives calculable corrections from R^3 terms.
- Quantum corrections preserve the universality of the bending angle.
- Deformations like Phi R^2 influence graviton bending in string-inspired models.

## 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 $\Phi R^2$, where $\Phi$ 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.