Electron Yukawa suppression of Higgs production ($y_e=\sqrt{2}{m}_e/v,g_{hee}=m_e/v$)

With the conventional electroweak vacuum value $v\simeq 246\mathrm{GeV}$, the Electron Yukawa coupling is $y_e\simeq 2.9\times 10^{-6}$ and the physical Higgs-electron vertex coefficient is $m_e/v\simeq 2.1\times 10^{-6}$. Direct s-channel Higgs production in electron-positron annihilation is consequently very small away from a compensating resonance enhancement. This suppression belongs to the coupling at the initial vertex, not to a prohibition on the Higgs boson coupling to W bosons.