Past exam of the advanced quantum field theory for particle physics course of the University of Oxford / 2016 / 1 / b / ii

Use the fundamental SU(3) normalization $\mathrm{tr}(T^a{T}^b)={\delta }^{ab}/2$, with Hermitian generators. The average over the $3\times 3$ incoming colours and sum over the outgoing colours givesThe complete spin and colour averaged result is consequentlyFor massless two-body centre-of-momentum kinematics, $t=-s(1-\cos \theta )/2$ and $u=-s(1+\cos \theta )/2$, so the same answer is $2g_s^4(1+{\cos }^2\theta )/9$. This checks positivity, the symmetry under exchanging the outgoing directions, and the absence of a forward $t$-channel singularity in this particular process.