$e^+e^- \to ZH$ at NLO EW matched to a QED parton shower

To prepare for the next generation particle collider, likely to be a high-energy precision-frontier electron-positron machine, theoretical predictions must improve in tandem. One aspect in which it is necessary to build on the progress made at LEP and at low-energy $e^+e^-$ colliders is in the modelling of initial-state QED radiation from leptons. In this paper we combine the MC@NLO parton shower matching method with QED resummation methods such as the electron structure function to obtain an automated, process-independent NLO-matched QED parton shower. The case of an electron-positron collider provides a particular challenge to the method due to the integrable singularity present in the lepton structure function, at variance with QCD PDFs. We develop new methods to allow a standard dipole parton shower to operate in the presence of this singularity. We validate the method by examining its dependence on infrared parameters and by verifying both the NLO-correctness, and the resummation properties, of the MC@NLO prediction. Finally, we present results for the case of Higgs production in association with an on-shell $Z$ boson at two proposed FCC-ee energies, the first such predictions at EW NLO+PS accuracy.