The Future Circular Collider (FCC-ee) offers the unique opportunity of studying the Higgs Yukawa coupling to the electron, $$y_\mathrm {e}$$
y
e
, via resonant s-channel production, $$\mathrm {e^+e^-}\rightarrow \mathrm {H}$$
e
+
e
-
→
H
, in a dedicated run at $$\sqrt{s} = m_\mathrm {H}$$
s
=
m
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 $$\mathrm {Z}^*$$
Z
∗
, $$\gamma ^*$$
γ
∗
, 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 $$y_\mathrm {e}$$
y
e
coupling and correspondingly small cross section: $$\sigma _\mathrm {ee\rightarrow H} \propto m_\mathrm {e}^2 = 0.57$$
σ
ee
→
H
∝
m
e
2
=
0.57
fb accounting for initial-state $$\gamma $$
γ
radiation. Second, the $$\mathrm {e^+e^-}$$
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, $$\varGamma _\mathrm {H} = 4.1$$
Γ
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, $$\sqrt{s} = m_\mathrm {H}$$
s
=
m
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: $$\mathrm {H}\rightarrow gg$$
H
→
g
g
and $$\mathrm {H}\rightarrow \mathrm {W}\mathrm {W}^*\!\rightarrow \ell \nu $$
H
→
W
W
∗
→
ℓ
ν
+ 2 jets. For a benchmark monochromatization with 4.1-MeV c.m. energy spread (leading to $$\sigma _\mathrm {ee\rightarrow H} = 0.28$$
σ
ee
→
H
=
0.28
fb) and 10 ab$$^{-1}$$
-
1
of integrated luminosity, a $$1.3\sigma $$
1.3
σ
signal significance can be reached, corresponding to an upper limit on the e$$^\pm $$
±
Yukawa coupling at 1.6 times the SM value: $$|y_\mathrm {e}|<1.6|y^\mathrm {\textsc {sm}}_\mathrm {e}|$$
|
y
e
|
<
1.6
|
y
e
S
M
|
at 95% confidence level, per FCC-ee interaction point per year. Directions for future improvements of the study are outlined.