Distinct-flavor quark scattering color factor ($\overline{|\mathcal{M}{|}^2}=4g_s^4(s^2+u^2)/(9t^2)$)

For massless distinguishable quarks exchanging one gluon, summing the squared generator contraction gives two with $\mathrm{Tr}(T^a{T}^b)={\delta }^{ab}/2$. Averaging nine initial colors and four initial spins leaves the coefficient $1/18$ multiplying the two Dirac traces. Their contraction is $8(s^2+u^2)$, yielding the displayed tree-level result. Identical quarks require an additional exchange amplitude and its interference.