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The worldline effective field theory (EFT) gives a gauge-invariant definitionof black hole conservative tidal responses (Love numbers), dissipation numbers,and their spin-0 and spin-1 analogs. In the first part of this paper we showhow the EFT allows us to circumvent the source/response ambiguity withouthaving to use the analytic continuation prescription. The source/responseambiguity appears if Post-Newtonian (PN)corrections to external sources overlapwith the response. However, these PN corrections can be clearly identified andisolated using the EFT. We illustrate that by computing static one-pointfunctions of various external fields perturbing the four-dimensionalSchwarzschild geometry. Upon resumming all relevant Feynman diagrams, we findthat the PN terms that may mimic the response actually vanish for static blackholes. Thus, the extraction of Love numbers from matching the EFT and generalrelativity (GR) calculations is completely unambiguous, and it implies that theLove numbers vanish identically for all types of perturbations. We also studyin detail another type of fine tuning in the EFT, the absence of Love numbers'running. We show that logarithmic corrections to Love numbers do stem fromindividual loop diagrams in generic gauges, but cancel after all diagrams aresummed over. In the particular cases of spin-0 and spin-2 fields the logarithmsare completely absent if one uses the Kaluza-Klein metric decomposition. In thesecond part of the paper we compute frequency-dependent dissipative responsecontributions to the one-point functions using the Schwinger-Keldysh formalism.We extract black hole dissipation numbers by comparing the one-point functionsin the EFT and GR. Our results are in perfect agreement with those obtainedfrom a manifestly gauge-invariant matching of absorption cross-sections.

Black Hole Tidal Love Numbers and Dissipation Numbers in Worldline Effective Field Theory