Model-independent ZH production cross section at FCC-ee

This paper presents prospects for measuring the model-independent $ZH$ production cross section at the FCC-ee using the recoil-mass method at center-of-mass energies of $240$ GeV and $365$ GeV. Analyses are carried out in the muon, electron, and hadronic decay modes of the associated $Z$ boson. The event selections rely primarily on the kinematics of the reconstructed $Z$ decay products, ensuring maximal independence from specific Higgs boson decay modes, while multivariate techniques are employed to further enhance sensitivity. Statistical interpretations of the individual final states yield relative precisions of $0.52\mathrm{\%}$ for the combined leptonic channels and $0.38\mathrm{\%}$ for the hadronic channel at $240$ GeV with an integrated luminosity of $10.8$ ab${}^{-1}$. Their full statistical combination leads to total uncertainties of $0.31\mathrm{\%}$ at $240$ GeV and $0.52\mathrm{\%}$ at $365$ GeV with $3.12$ ab${}^{-1}$. Dedicated statistical tests demonstrate model independence at the level of the obtained precision. This study presents the first consistent and combined analysis of the leptonic and hadronic final states for a model-independent $ZH$ cross-section measurement at a future lepton collider, using a unified workflow and covering both $\sqrt{s}=240$ and $365$ GeV. It provides the most precise expected measurement of the $ZH$ production cross section at future lepton colliders, with the degree of model independence demonstrated within the achieved statistical precision.