  We match scattering amplitudes in point particle effective field theory (EFT)
and general relativity to extract low frequency dynamical tidal responses of
rotating (Kerr) black holes to all orders in spin. In the conservative sector,
we study local worldline couplings that correspond to the time-derivative
expansion of the black hole tidal response function. These are dynamical
(frequency-dependent) generalizations of the static Love numbers. We identify
and extract couplings of three types of subleading local worldline operators:
the curvature time derivative terms, the spin - curvature time derivative
couplings, and quadrupole - octupole mixing operators that arise due to the
violation of spherical symmetry. The first two subleading couplings are
non-zero and exhibit a classical renormalization group running; we explicitly
present their scheme-independent beta functions. The conservative mixing terms,
however, vanish as a consequence of vanishing static Love numbers. In the
non-conservative sector, we match the dissipation numbers at next-to-leading
and next-to-next-to leading orders in frequency. In passing, we identify terms
in the general relativity absorption probabilities that originate from tails
and short-scale logarithmic corrections to the lowest order dissipation
contributions.
