Dimension-six electroweak top-loop effects in Higgs production and decay

We study the next-to-leading order electroweak corrections to Higgs processes from dimension-six top-quark operators in the Standard Model Effective Field Theory approach. We consider the major production channels, including $WH$, $ZH$, and VBF production at the LHC, and $ZH$, VBF production at future lepton colliders, as well as the major decay channels including $H\to \gamma\gamma, \gamma Z, Wl\nu,Zll,b\bar b,\mu\mu,\tau\tau$. The results show that within the current constraints, top-quark operators can shift the signal strength of the loop-induced processes, i.e. $H\to \gamma\gamma,\gamma Z$, by factors of $\sim\mathcal{O}(1)-\mathcal{O}(10)$, and that of the tree-level processes, i.e. all remaining production and decay channels, by $\sim5-10\%$ at the LHC, and up to $\sim15\%$ at future lepton colliders. This implies that essentially all Higgs channels have started to become sensitive to top-quark couplings, and in particular, Higgs observables at high luminosity LHC as well as future lepton colliders, even below the $t\bar t$ threshold, will improve our knowledge of top-quark couplings. We derive the sensitivities of Higgs measurements to top-quark operators at the high luminosity LHC, using projections for both inclusive and differential measurements. We conclude that treating the dimension-six top-quark sector and the Higgs/electroweak sector separately may not continue to be a good strategy. A global analysis combining Higgs and top-quark measurements is desirable, and our calculation and implementation provide an automatic and realistic simulation tool for this purpose.