Dipolar tidal effects in gravitational waves from scalarized black hole binary inspirals in quadratic gravity

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.