The Higgs Self-Coupling at FCC-ee

Single Higgs production at FCC-ee probes the Higgs self-coupling at next-to-leading order (NLO). Extracting a bound requires a global analysis accounting for other possible new physics contributions up to NLO. We determine the FCC-ee sensitivity to Higgs self-coupling modifications $\delta\kappa_\lambda$ within the Standard Model Effective Field Theory (SMEFT) framework, including for the first time flavour, LEP, LHC, and FCC-ee observables in a global analysis with all leading NLO effects via one-loop renormalisation group evolution, as well as incorporating finite NLO contributions to electroweak precision and $ZH$ observables. The global sensitivity to $\delta\kappa_\lambda$ is estimated by marginalising over the effects of all other operators, bringing flavour considerations to the fore. We find that, under reasonable assumptions, FCC-ee sensitivity to $\delta\kappa_\lambda$ can exceed that of the HL-LHC.