Love beyond Einstein: Metric reconstruction and Love number in quadratic gravity using WEFT

Abstract: We study tidal Love numbers of static black holes in four-dimensional quadratic theory of gravity, extending the result of GR. We use worldline effective field theory (WEFT) methods to compute metric perturbations from one-point functions, treating the higher-derivative terms perturbatively. We show that insertions of scalar fields on the worldline induce non-zero tidal tails, and the corresponding Love number displays no RG running. The same conclusion holds for the insertions of tensor fields. Furthermore, for scalar dipole perturbations, we derive a Yukawa-deformed Frobenius solution and match the asymptotic behavior to fix the UV charge, finding agreement with EFT predictions of Wilson coefficients. Our work demonstrates that quadratic higher-curvature corrections induce non-zero but scale-independent tidal responses, offering a robust EFT framework to test deviations from GR in gravitational wave observations.