Abstract
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 the curvature tensor. Scattering amplitudes in momentum and position space provide systematic complementary approaches. For the tidal operators quadratic in curvature, which describe the linear response to an external gravitational field, we work out the leading post-Minkowskian contributions using a basis of operators with arbitrary numbers of derivatives which are in one-to-one correspondence with the worldline multipole operators. Explicit examples are used to show that the same techniques apply to both bodies interacting tidally with a spinning particle, for which we find the leading contributions from quadratic in curvature tidal operators with an arbitrary number of derivatives, and to effective field theory extensions of general relativity. We also note that the leading post-Minkowskian order contributions from higher-dimension operators manifest double-copy relations. Finally, we comment on the structure of higher-order corrections.
Highlights
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 the curvature tensor
For the tidal operators quadratic in curvature, which describe the linear response to an external gravitational field, we work out the leading post-Minkowskian contributions using a basis of operators with arbitrary numbers of derivatives which are in one-to-one correspondence with the worldline multipole operators
Explicit examples are used to show that the same techniques apply to both bodies interacting tidally with a spinning particle, for which we find the leading contributions from quadratic in curvature tidal operators with an arbitrary number of derivatives, and to effective field theory extensions of general relativity
Summary
In this work we study tidal or finite-size effects in the gravitational interactions of two massive extended bodies. From our point of view, the new scale Rs is introduced by integrating out the degrees of freedom that describe the tidal dynamics of an extended body to yield a point-particle effective theory In such an effective theory the finite size effects are encoded as higherdimension operators Oi which are suppressed by powers of Rs|q|. Their Wilson coefficients can be determined either by matching to the complete theory that includes the tidal degrees of freedom, or by comparing to experiment. A side effect of choosing Rs instead of R as the scale characterizing finite-size effects is that for less compact bodies the Wilson coefficients are not necessarily O(1) This approach was pioneered in the context of a worldline PN formalism in ref.
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