Color average (${\overline{|\mathcal{M}{|}^2}}_{\mathrm{color}}=N^{-2}{\sum }_{i,j,k,l}|{\mathcal{M}}_{ij;kl}{|}^2$)

A uniform incoherent initial mixture of two independently prepared fundamental color charges requires an average over their $N^2$ initial possibilities, together with a sum over unobserved final color charges. This differs from preparing a coherent color singlet. For quark-antiquark annihilation through one vector in the adjoint representation, $c_s=T_{ji}^a{T}_{kl}^a$ gives $N^{-2}\sum |c_s{|}^2=(N^2-1)/(4N^2)$. For the exchange contraction $c_t=T_{ki}^a{T}_{jl}^a$, $N^{-2}\sum c_s{c}_t^{\ast }=-(N^2-1)/(4N^3)$ by the SU(N) fundamental completeness relation. The negative overlap reverses the sign of the corresponding Abelian interference term.

In distinct-flavour quark annihilation, the one-photon exchange color charge tensor is ${\delta }_{ji}{\delta }_{kl}$, whereas the one-gluon tensor is ${\sum }_A{T}_{ji}^A{T}_{kl}^A$. Their inner product after the external color charge sum is ${\sum }_A\mathrm{tr}(T^A)\mathrm{tr}(T^A)=0$, since the fundamental gauge generators of $SU(3)$ are traceless. Thus the averaged squared scattering amplitude has no leading electromagnetic–strong interference term for this process. Fixed external color charge components, or processes with different exchange pairings, need not share this cancellation.