Pair production (t-channel)

Perturbative order$\alpha$ (tree level)
Topologyt-channel
Symmetry factorCounts overcounting in the perturbation series. If a diagram has internal symmetries—ways to relabel internal lines and get the same diagram back—the symmetry factor divides that out. Most QED diagrams have S=1; the vacuum polarization bubble has S=1/2 because swapping the two internal fermion lines gives the same diagram.1.0
Divergence finite

Contributes to

Pair production

An incoming photon produces a virtual electron, which absorbs the second photon and produces the outgoing electron-positron pair. Related to pair annihilation by time reversal and to Compton scattering by crossing.

The computational chain

From diagram to number—every step of the amplitude calculation.

The diagram
An incoming photon produces a virtual electron, which absorbs the second photon and produces the outgoing $e^+e^-$ pair. Related to pair annihilation by time reversal and to Compton scattering by crossing: $s_{\text{Compton}} \to t_{\text{production}}$.
Crossing relation
$$|\mathcal{M}(\gamma\gamma \to e^+e^-)|^2 = |\mathcal{M}(e^+e^- \to \gamma\gamma)|^2\bigg|_{s\leftrightarrow t}$$
The squared amplitude is identical to pair annihilation with Mandelstam variables relabeled. The cross section differs because the flux factor and phase space depend on the initial state.

Related diagrams

Crossing Symmetry

Exchange Symmetry