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  • Open Access

Classical gravitational scattering with a massive scalar mediator

Birgitta Biendarra*, Kays Haddad†, and Jan Plefka‡

  • *Contact author: birgitta.biendarra@hu-berlin.de
  • †Contact author: kays.haddad@physik.hu-berlin.de
  • ‡Contact author: jan.plefka@hu-berlin.de
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Phys. Rev. D 114, 084033 – Published 9 October, 2026

DOI: https://doi.org/10.1103/7hmw-9fx7

Abstract

We consider the classical scattering of two gravitating compact objects in the presence of a massive scalar mediator, providing a simple model of exotic phenomena. Through dimensional analysis, we argue that such a process can only be classical in the presence of gravity, a consequence of which is that perturbing in the coupling of the scalar to a worldline is not separate from the post-Minkowskian expansion. When computing asymptotic observables, the massive mediator complicates the Fourier transforms to impact-parameter space at next-to-leading order. We reduce these to univariate parametric integrals—amenable to numerical integration—and produce analytic results for the linear impulse and the scattering angle to the second post-Minkowskian order. The scattering angle exhibits a maximum when the range of the scalar-mediated force is comparable to the impact parameter, a possible signature of a massive scalar mediator. In the opposite, large-mass regime we uncover a screening effect: integrating out the scalar sourced by each compact object reduces its gravitational mass by an amount linear in the scalar’s mass. Both of these phenomena are next-to-leading-order effects.

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Phys. Rev. D 114, 084033– Published 9 October, 2026
  • Received 24 August 2026
  • Accepted 22 September 2026
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