Quasi-Keplerian parametrization for compact binaries on hyperbolic orbits in scalar-tensor theories at second post-Newtonian order

We obtain the generalized quasi-Keplerian parametrization for compact binaries on quasihyperbolic orbits at second post-Newtonian (2PN) order in a class of massless scalar-tensor theories, extending the analogous results for quasielliptic systems arXiv:2401.06844. In particular, we compute the conservative scattering angle and impact parameter at 2PN. We explicitly confirm the 2PN conservative scatter-to-bound map in these theories between the scattering angle and the periastron advance. We then compute the total energy and angular momentum lost by the system. Flux-balance arguments then allow us to compute the dissipative contributions to the scattering angle at 1.5PN and 2.5PN, completing the full scattering angle at 2.5PN in these theories. Finally, we obtain, in general relativity, an expression for the 3PN impact parameter in the conservative sector, correcting previous literature.