Higgs boson coupling to W bosons ($g_{hWW}=2m_W^2/v$)

Expanding the Higgs doublet kinetic term about its vacuum expectation value gives $\mathcal{L}\supset (2m_W^2/v)h{W}_{\mu }^{+}{W}^{-\mu }$. Its vertex is proportional to $g_{\mu \nu }$, so scalar exchange contracts the external particle polarization vectors.