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Dynamical Tidal Response of Schwarzschild Black Holes

Dynamical Love numbers capture the conservative response of an object to a time-dependent external tidal gravitational field. We compute the dynamical Love numbers of Schwarzschild black holes in general relativity within a point-particle effective field theory framework. In addition to the known logarithmic running, we compute the finite scheme-dependent contributions to the Love number couplings. We do this by matching the renormalized one-point function in the effective theory to the classical field profile computed in general relativity. On the general relativity side, we solve the Regge-Wheeler and Zerilli equations perturbatively in a small frequency expansion. In order to match on the effective field theory side we include gravitational interactions using the Born series and employ dimensional regularization to obtain a renormalized field profile.