  The worldline effective field theory (EFT) gives a gauge-invariant definition
of 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 show
how the EFT allows us to circumvent the source/response ambiguity without
having to use the analytic continuation prescription. The source/response
ambiguity appears if Post-Newtonian (PN)corrections to external sources overlap
with the response. However, these PN corrections can be clearly identified and
isolated using the EFT. We illustrate that by computing static one-point
functions of various external fields perturbing the four-dimensional
Schwarzschild geometry. Upon resumming all relevant Feynman diagrams, we find
that the PN terms that may mimic the response actually vanish for static black
holes. Thus, the extraction of Love numbers from matching the EFT and general
relativity (GR) calculations is completely unambiguous, and it implies that the
Love numbers vanish identically for all types of perturbations. We also study
in 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 from
individual loop diagrams in generic gauges, but cancel after all diagrams are
summed over. In the particular cases of spin-0 and spin-2 fields the logarithms
are completely absent if one uses the Kaluza-Klein metric decomposition. In the
second part of the paper we compute frequency-dependent dissipative response
contributions to the one-point functions using the Schwinger-Keldysh formalism.
We extract black hole dissipation numbers by comparing the one-point functions
in the EFT and GR. Our results are in perfect agreement with those obtained
from a manifestly gauge-invariant matching of absorption cross-sections.
