Gravitational scattering up to third post-Newtonian approximation for conservative dynamics: Scalar-tensor theories

We compute the scattering angle $\ensuremath{\chi}$ for hyperboliclike encounters in massless scalar-tensor theories up to third post-Newtonian order for the conservative part of the dynamics. To calculate the gauge-invariant scattering angle as a function of energy and orbital angular momentum, we use the approach of effective-one-body formalism as introduced in Bini and Damour [Phys. Rev. D 96, 064021 (2017)]. We then compute the nonlocal-in-time contribution to the scattering angle by using the strategy of order reduction of nonlocal dynamics introduced for small-eccentricity orbits.