  The mass and spin of black holes (BHs) in binary systems may change due to
the infall of gravitational-wave (GW) energy down the horizons. For spinning
BHs, this effect enters at 2.5 post-Newtonian (PN) order relative to the
leading-order energy flux at infinity. There is currently a discrepancy in the
literature in the expressions of these horizon fluxes in the test-body limit at
4PN order (relative 1.5PN order). Here, we model the horizon absorption as
tidal heating in an effective worldline theory of a spinning particle equipped
with tidally-induced quadrupole and octupole moments. We match the tidal
response to analytic solutions of the Teukolsky equation in a scattering
scenario, and obtain general formulae for the evolution of mass and spin. We
then specialize to the case of aligned-spin--quasi-circular binaries, obtaining
the corresponding contributions to the GW phasing through 4PN order.
Importantly, we find that the number of GW cycles due to horizon fluxes with
masses observed by LIGO-Virgo-KAGRA detectors is about 2-3 orders of magnitude
smaller than the other contributions to the phasing at the same PN order.
Furthermore, in the test-body limit, we find full agreement with results
obtained earlier from BH perturbation theory, with a small mass in an
equatorial circular orbit treated as a source perturbing the Kerr metric. Thus,
we weigh in on one side of the previous discrepancy.
