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We compare numerical self-force results and analytical fourth-orderpost-Minkowskian (PM) calculations for hyperbolic-type scattering of apoint-like particle carrying a scalar charge $Q$ off a Schwarzschild blackhole, showing a remarkably good agreement. Specifically, we numerically computethe scattering angle including the full $O(Q^2)$ scalar-field self-force term(but ignoring the gravitational self-force), and compare with analyticalexpressions obtained in a PM framework using scattering-amplitude methods. Thisexample provides a nontrivial, high-precision test of both calculation methods,and illustrates the complementarity of the two approaches in the context of theprogram to provide high-precision models of gravitational two-body dynamics.Our PM calculation is carried out through 4PM order, i.e., including all termsthrough $O(Q^2 G^3)$. At the fourth post-Minkowskian order the point-particledescription involves two a-priori undetermined coefficients, due tocontributions from tidal effects in the model under consideration. Thesecoefficients are chosen to align the post-Minkowskian results with theself-force ones.

Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model