  Gravitational waves (GWs) from merging binary black holes (BHs) enable
unprecedented tests of gravitational theories beyond Einstein's General
Relativity (GR) in highly nonlinear, dynamical regimes. Such GW measurements
require an accurate description of GW signatures that may arise in alternative
gravitational models. In this work, we focus on a class of higher-curvature
extensions of GR, the scalar-Gauss-Bonnet theories, where BHs can develop
scalar hair. In an inspiraling binary system, this leads to scalar-induced
tidal effects in the dynamics and radiation. We calculate the dominant
adiabatic dipolar tidal effects via an approximation scheme based on expansions
in post-Newtonian, higher-curvature, and tidal corrections. The tidal effects
depend on a characteristic scalar Love number, which we compute using BH
perturbation theory, and have the same scaling with GW frequency as the
higher-curvature corrections. We perform case studies to characterize the net
size and parameter dependencies of these effects, showing that at low
frequencies, tidal effects dominate over the higher-curvature contributions for
small couplings within current bounds, regardless of the total BH mass, while
at high frequencies they are subdominant. We further consider prospects
observing both of these regimes, which would be interesting for breaking
parameter degeneracies, with multiband detections of LISA and ground-based
detectors or the Einstein Telescope alone. We also assess the frequency range
of the transition between these regimes by numerically solving the energy
balance law. Our results highlight the importance of the dipolar scalar tidal
effects for BHs with scalar hair, which arise in several beyond-GR paradigms,
and provide ready-to-use inputs for improved GW constraints on Gauss-Bonnet
theories.
