W boson propagator ($D_{\mu \nu }(p)=\frac{-i(g_{\mu \nu }-p_{\mu }{p}_{\nu }/M_W^2)}{p^2-M_W^2+i0}$)

In unitary gauge, the free massive W boson has the displayed momentum-space propagator. At external momentum small compared with $M_W$, its leading term is $i{g}_{\mu \nu }/M_W^2$. Inserting it between two weak charged current vertices produces the local Fermi interaction, with $G_F/\sqrt{2}=g^2/(8M_W^2)$ when each vertex is written with $1-{\gamma }_5$. Higher momentum terms give higher-dimensional operators; other gauges distribute the longitudinal contribution differently while giving the same physical amplitudes.