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We propose differential observables for $pp \to Z(\ell^+\ell^-)h(b\bar{b})$that can be used to completely determine the tensor structure of the$hZZ^*/hZ\bar{f}f$ couplings relevant to this process in the dimension-6 SMEFT.In particular, we propose a strategy to probe the anomalous $h Z_{\mu\nu}Z^{\mu \nu}$ and $h Z_{\mu \nu}\tilde{Z}^{\mu \nu}$ vertices at the percentlevel. We show that this can be achieved by resurrecting the interference termbetween the transverse $Zh$ amplitude, which receives contributions from theabove couplings, and the dominant SM longitudinal amplitude. Thesecontributions are hard to isolate without a knowledge of the analyticalamplitude, as they vanish unless the process is studied differentially in threedifferent angular variables at the level of the $Z$-decay products. By alsoincluding the differential distributions with respect to energy variables, weobtain projected bounds for the two other tensor structures of the Higgscoupling to $Z$-bosons.

Resolving the tensor structure of the Higgs coupling to $Z$-bosons via Higgs-strahlung