In superconductors the Anderson-Higgs mechanism allows for the existence of a collective amplitude (Higgs) mode which can couple to light only in a non-linear Raman-like process. While the observed properties of the Higgs mode in conventional, isotropic superconductors can be explained in a mean-field picture, strong interaction effects with other modes in anisotropic d-wave superconductors are likely. Here we calculate the Raman contribution of the Higgs mode from a new perspective, including many-body Higgs oscillations effects and their consequences in steady-state Raman spectroscopy. This solves the long-standing problem of the A1g symmetry Raman spectrum in d-wave superconductors. In order to test our theory, we predict the presence of measurable characteristic oscillations in THz quench-optical probe time-dependent reflectivity experiments.
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