The photon PDF in events with rapidity gaps

We consider photon-initiated events with large rapidity gaps in proton-proton collisions, where one or both protons may break up. We formulate a modified photon PDF that accounts for the specific experimental rapidity gap veto, and demonstrate how the soft survival probability for these gaps may be implemented consistently. Finally, we present some phenomenological results for the two-photon induced production of lepton and $W$ boson pairs.