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We present a framework to compute amplitudes for the gravitational analog ofthe Raman process, a quasi-elastic scattering of waves off compact objects, inworldline effective field theory (EFT). As an example, we calculate thirdpost-Minkowskian (PM) order ($\mathcal{O}(G^3)$), or two-loop, phase shifts forthe scattering of a massless scalar field including all tidal effects anddissipation. Our calculation unveils two sources of the classicalrenormalization-group flow of dynamical Love numbers: a universal runningindependent of the nature of the compact object, and a running self-induced bytides. Restricting to the black hole case, we find that our EFT phase shiftsagree exactly with those from general relativity, provided that the relevantstatic Love numbers are set to zero. In addition, we carry out a completematching of the leading scalar dynamical Love number required to renormalize auniversal short scale divergence in the S-wave. Our results pave the way forsystematic calculations of gravitational Raman scattering at higher PM orders.

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