Gravitational Raman Scattering in Effective Field Theory: a Scalar Tidal Matching at $\mathcal{O}(G^3)$

Understand

We present a framework to compute amplitudes for the gravitational analog of the Raman process, a quasi-elastic scattering of waves off compact objects, in worldline effective field theory (EFT).

• As an example, we calculate third post-Minkowskian (PM) order ($\mathcal{O}(G^3)$), or two-loop, phase shifts for the scattering of a massless scalar field including all tidal effects and dissipation.
• Our calculation unveils two sources of the classical renormalization-group flow of dynamical Love numbers: a universal running independent of the nature of the compact object, and a running self-induced by tides.
• Restricting to the black hole case, we find that our EFT phase shifts agree exactly with those from general relativity, provided that the relevant static Love numbers are set to zero.