 Electron Yukawa suppression of Higgs production

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.