Matching Tidal Deformability (Wilson) Coefficients to Black Hole Love Numbers in Higher-Curvature Gravity

We present a consistent mapping between tidal deformability coefficients (tidal Love numbers) and Wilson coefficients in effective field theory (EFT) descriptions of higher-curvature theories of gravity. In this work, we focus on the connection between the static response of a non-spinning black hole and the corresponding Wilson coefficient governing tidal imprints in gravitational-wave signals. We analyze a set of control cases to identify the key ingredients required for a systematic computation and matching procedure. In doing so, we highlight shortcomings in existing results that rely on the standard matching approach used in General Relativity when applied to higher-curvature gravity theories. As an explicit demonstration, we compute the relevant coefficients for cubic gravity theories. Our findings bridge an important gap in the correspondence between tidal Love numbers and Wilson coefficients in EFT extensions of General Relativity, which had not been thoroughly explored previously.