Black holes in Einstein-scalar-Gauss-Bonnet model probed with scattering amplitudes

We examined the quantum properties of scalar-tensor gravity with a coupling to the Gauss-Bonnet term in the low-energy limit, exploring both linear and quadratic couplings. We calculated the leading-order corrections to the nonrelativistic one-body gravitational potential and the metric by studying the gravitational field of a pointlike scalar particle. We studied lightlike scattering and compared it with the classical theory. We found that the nonminimal coupling does not contribute to the small-angle scattering for the quadratic coupling but does in the case of linear coupling. The results provide an opportunity to constrain the linear nonminimal coupling to the Gauss-Bonnet term with forthcoming observational data.