= Non-Abelian Ward identity for fermion annihilation
{title2=$k_{2\nu}\mathcal M^{ab\mu\nu}\propto k_1^\mu$}
For a <Dirac field> annihilating with its antiparticle into two massless <gauge bosons>, the two ordered fermion-exchange diagrams leave a colour <matrix commutator> when one outgoing momentum contracts the <scattering amplitude>. The three-boson exchange diagram cancels this current term but leaves a term proportional to the other outgoing momentum. With $D=\partial-igA$, $J_c^\lambda=\bar v\gamma^\lambda t^cu$, $q=k_1+k_2$, and the source's positive-sign three-boson vertex, the tree result is $k_{2\nu}\mathcal M^{ab\mu\nu}=ig^2f^{abc}(J_c\cdot k_2)k_1^\mu/q^2$. It vanishes after contraction with a physical <polarization vector> on leg 1, although the open-index tensor is generally nonzero.
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