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

We calculate the dominant contributions of third generation four-quark operators to single-Higgs production and decay. They enter via loop corrections to Higgs decays into gluons, photons and $b\bar{b}$, and in Higgs production via gluon fusion and in association with top quark pairs. We show that these loop effects can, in some cases, lead to better constraints than those from fits to top quark data. Finally, we investigate whether these four-fermion operators can spoil the determination of the trilinear Higgs self-coupling from fits to single-Higgs data.