Measurement of CKM element $\mathrm{\mid }{V}_{cb}\mathrm{\mid }$ from $W$ boson decays at the future Higgs factories

This study investigates the precision measurement of the CKM matrix element $\mathrm{\mid }{V}_{cb}\mathrm{\mid }$ through semileptonic $WW$ events at future Higgs factories, $i\mathrm{.}e\mathrm{.}$, FCC-ee, ILC, C${}^3$, and CEPC. We use full detector simulation to generate the $WW\to \mathrm{\ell }\nu cb$ signal events and various backgrounds at $\sqrt{s}=240$ GeV with unpolarized beams. The relative statistical uncertainties are projected to be 0.91% for the muon channel and 1.2% for the electron channel, assuming a baseline integrated luminosity of 5 ab${}^{-1}$. The sensitivities at other Higgs factory scenarios are also projected. Possible contributors to systematic uncertainties are discussed, with the most prominent one being the systematics of flavor-tagging and mistagging rates. Combining with $WW$ threshold runs, the relative systematic uncertainty can be further reduced.