Heterotic footprints in classical gravity: PM dynamics from on-shell soft amplitudes at one loop

A bstract We study classical scattering of charged black holes in Einstein-Maxwell-Dilaton (EMD) theory. Working in the classical (Post-Minkowskian) regime, we extract the conservative two-body potential by expanding the one-loop amplitudes in the soft regime. We explicitly show that, as in GR, the relevant soft amplitudes are infrared (IR) finite when long-range interactions are consistently treated via the Lippmann-Schwinger equation and the associated IR subtraction. The scattering angle is then obtained from the eikonal exponentiation of the soft amplitude. Our results track the separate roles of electromagnetic and dilatonic charges in both the conservative dynamics and the eikonal phase, and they smoothly reduce to the GR limit when the charges and the dilaton coupling are switched off. Where applicable, we compare our results with existing literature and find agreement. These findings provide amplitude-based benchmarks for compact-object dynamics in EMD and furnish building blocks for waveform modeling in beyond-GR scenarios.