Measuring the electron Yukawa coupling via resonant s-channel Higgs production at FCC-ee

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: $\sigma _\mathrm {ee\rightarrow H} \propto m_\mathrm {e}^2 = 0.57$ 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 $\sigma _\mathrm {ee\rightarrow H} = 0.28$ fb) and 10 ab$^{-1}$ of integrated luminosity, a $1.3\sigma $ 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.