Electron-positron annihilation into a quark pair (${\sigma }_q=4\pi {\alpha }^2{Q}_q^2/s$)

For massless quarks at photon-exchange tree level, the initial-spin-averaged, final-color-summed amplitude is $\overline{|\mathcal{M}{|}^2}=8N_c{e}^4{Q}_q^2[(p_1\cdot q_1)(p_2\cdot q_2)+(p_1\cdot q_2)(p_2\cdot q_1)]/s^2$. In the centre-of-mass frame this is $N_c{e}^4{Q}_q^2(1+{\cos }^2\theta )$. With $N_c=3$ and the standard two-body flux, its integrated cross-section is the displayed result.