Higgs probes of top contact interactions and their interplay with Higgs self-coupling

We present a method which relies on loop contributions from four-top SMEFT operators to single Higgs observables to contrain their Wilson coefficients. Such loop-induced terms have a non-trivial interplay with the extraction of the trilinear Higgs coupling. We show that this strategy can, for some operators, lead to more stringent bounds than direct measurement via top quark data. Finally, we mention some recent developements in the treatment of $\gamma_5$ in dimensional regularisation in the context of the SMEFT.