  We present the results of the new SuperChic 4 Monte Carlo implementation of
photon-initiated production in proton-proton collisions, considering as a first
example the case of lepton pair production. This is based on the structure
function calculation of the underlying process, and focusses on a complete
account of the various contributing channels, including the case where a
rapidity gap veto is imposed. We provide a careful treatment of the
contributions where either (single dissociation), both (double dissociation) or
neither (elastic) proton interacts inelastically and dissociates, and interface
our results to Pythia for showering and hadronization. The particle decay
distribution from dissociation system, as well the survival probability for no
additional proton-proton interactions, are both fully accounted for; these are
essential for comparing to data where a rapidity gap veto is applied. We
present detailed results for the impact of the veto requirement on the
differential cross section, compare to and find good agreement with ATLAS 7 TeV
data on semi-exclusive production, and provide a new precise evaluation of the
background from semi-exclusive lepton pair production to SUSY particle
production in compressed mass scenarios, which is found to be low.
