Massless quark Compton scattering ($\overline{|\mathcal{M}{|}^2}=-2e^4{Q}_q^4(s/u+u/s)$)

The two electromagnetic tree-level Feynman diagrams for $q\gamma \to q\gamma$ exchange a quark in the $s$ and $u$ channels. Their sum obeys both photon Ward identities. Averaging over the initial quark spin, color charge and two physical incoming photon polarization vectors gives $-2e^4{Q}_q^4(s/u+u/s)$ after final-state sums. The color average is one because the interaction preserves the single open quark colour index. The interference trace is proportional to $(p_1+p_2)\cdot (p_1-p_4)=(s+t+u)/2=0$ for massless external states.