The Future Circular Collider (FCC-ee) offers the unique opportunity of studying the Higgs Yukawa coupling to the electron, y_mathrm {e}, via resonant s-channel production, mathrm {e^+e^-}rightarrow mathrm {H}, in a dedicated run at sqrt{s} = m_mathrm {H}. The signature for direct Higgs production is a small rise in the cross sections for particular final states, consistent with Higgs decays, over the expectations for their occurrence due to Standard Model (SM) background processes involving mathrm {Z}^*, gamma ^*, or t-channel exchanges alone. Performing such a measurement is remarkably challenging for four main reasons. First, the low value of the e^pm mass leads to a tiny y_mathrm {e} coupling and correspondingly small cross section: sigma _mathrm {eerightarrow H} propto m_mathrm {e}^2 = 0.57 fb accounting for initial-state gamma radiation. Second, the mathrm {e^+e^-} beams must be monochromatized such that the spread of their centre-of-mass (c.m.) energy is commensurate with the narrow width of the SM Higgs boson, varGamma _mathrm {H} = 4.1 MeV, while keeping large beam luminosities. Third, the Higgs mass must also be known beforehand with a few-MeV accuracy in order to operate the collider at the resonance peak, sqrt{s} = m_mathrm {H}. Last but not least, the cross sections of the background processes are many orders-of-magnitude larger than those of the Higgs decay signals. A preliminary generator-level study of 11 Higgs decay channels using a multivariate analysis, which exploits boosted decision trees to discriminate signal and background events, identifies two final states as the most promising ones in terms of statistical significance: mathrm {H}rightarrow gg and mathrm {H}rightarrow mathrm {W}mathrm {W}^*!rightarrow ell nu + 2 jets. For a benchmark monochromatization with 4.1-MeV c.m. energy spread (leading to sigma _mathrm {eerightarrow H} = 0.28 fb) and 10 ab^{-1} of integrated luminosity, a 1.3sigma signal significance can be reached, corresponding to an upper limit on the e^pm Yukawa coupling at 1.6 times the SM value: |y_mathrm {e}|<1.6|y^mathrm {textsc {sm}}_mathrm {e}| at 95% confidence level, per FCC-ee interaction point per year. Directions for future improvements of the study are outlined.
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