Past exam of the particle physics course of the University of Oxford / 2022 / 1 / e

The intermediate photon carries spin $J=1$. In the massless limit, a back-to-back fermion-antifermion pair coupled to its vector current has opposite helicities, so the initial and final projections along their respective axes are $m,m^{\prime }=\pm 1$. A rotation between these axes contributes the Wigner D-matrix elements $d_{m^{\prime }m}^1(\theta )$. The relevant elements have magnitudes $(1+\cos \theta )/2$ and $(1-\cos \theta )/2$. Summing the four squared helicity amplitudes gives the angular factorThe common coupling and normalization factors recover the result in d. The $m=0$ terms do not contribute: the massless external vector currents eliminate the corresponding helicity configurations.