Expected precision of Higgs boson decays to two photons and Z boson with a photon at the FCC-ee

Despite the small branching fractions of H → γγ and H → Zγ, the clean environment of electron-positron collisions enables the measurement of their cross-sections and branching ratios with a precision comparable to that expected from the HL-LHC. This note presents an analysis of the cross-section measurement and expected uncertainties at √s = 240 and 365 GeV for the ZH production mode, as well as the vector boson fusion production mode at 365 GeV. The analysis employs a basic cut-based approach with a categorization of the associated Z boson decay, further enhanced using machine learning techniques. Results are interpreted under different assumptions for the electromagnetic calorimeter resolution.