Precision measurements of the Higgs boson decays in $e^{+}e^{-}\!\to Z(\ell\ell)H$ with $H\!\to WW^{*}\!\to \ell u\ell u$ at the FCC-ee

This note presents a feasibility study of the measurement of $\sigma(e^+e^-\to ZH)\times\mathcal{B}(H\to WW^*)$ in the fully leptonic $Z(\ell\ell)H$, $H\to WW^*\to\ell\nu\ell\nu$ (where $\ell = e,\mu$) final state at FCC-ee. The study uses Monte Carlo samples processed through a parameterized simulation of the IDEA detector concept. Separate analyses are performed for projected integrated luminosities of $10.8~\mathrm{ab}^{-1}$ at $\sqrt{s}=240$ GeV and $3.12~\mathrm{ab}^{-1}$ at $\sqrt{s}=365$ GeV. Events are reconstructed from four charged leptons (electrons and/or muons) and missing momentum, selected using kinematic requirements, and classified with boosted decision trees. A binned likelihood fit to the classifier output gives expected relative precisions of 3.09% and 7.33% at 240 and 365 GeV, respectively, and 2.90% for their combination.