Sudakov effects in photon-initiated processes

We consider the effect of the Sudakov factor in photon-initiated processes, corresponding to the no branching probability for the initial-state photon. We demonstrate how such a factor follows simply from the solution of the DGLAP equation for the photon PDF, and is therefore included automatically by this. We use this result to argue that the appropriate scale for the QED coupling $\alpha$ associated with an initial-state photon is not the virtuality of the photon, but rather the factorization scale at which the photon PDF is evaluated, and therefore that the use of the on-shell renormalization scheme is not appropriate for such processes. We also discuss exclusive photon-initiated processes, and demonstrate that no explicit Sudakov factor is required in this case.