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

TL;DR

This paper investigates how quadratic curvature corrections in gravity theories affect black hole tidal responses, using effective field theory methods to compute Love numbers and their scale independence, providing insights for gravitational wave tests.

Contribution

It introduces a perturbative EFT approach to compute tidal Love numbers in quadratic gravity, revealing non-zero, scale-independent responses and matching asymptotic behaviors with EFT predictions.

Findings

Quadratic gravity induces non-zero tidal Love numbers.

Love numbers show no RG running, remaining scale-independent.

The EFT framework matches asymptotic behaviors with Wilson coefficients.

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.