Leading nonlinear tidal effects and scattering amplitudes

A bstract We present the two-body Hamiltonian and associated eikonal phase, to leading post-Minkowskian order, for infinitely many tidal deformations described by operators with arbitrary powers of curvature tensor. Scattering amplitudes in momentum position space provide systematic complementary approaches. For quadratic curvature, which describe linear response an external gravitational field, we work out contributions using a basis numbers derivatives are one-to-one correspondence worldline multipole operators. Explicit examples used show that same techniques apply both bodies interacting tidally spinning particle, find from number derivatives, effective field theory extensions general relativity. also note order higher-dimension manifest double-copy relations. Finally, comment on structure higher-order corrections.