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We discuss photon-photon fusion mechanisms of dilepton production inproton-proton collisions with rapidity gap in the main detector and one forwardproton in the forward proton detectors. This is relevant for the LHCmeasurements by ATLAS+AFP and CMS+PPS. Transverse momenta of the intermediatephotons are taken into account and photon fluxes are expressed in terms ofproton electromagnetic form factors and structure functions. Differentialdistributions in $\xi_{1/2}$, $M_{ll}$, $Y_{ll}$, $p_{t,ll}$, $M_R$ %pamietacwyjasnic M_R w tekscie are shown and the competition of different mechanisms isdiscussed. Both double-elastic and single-dissociative processes are includedin the analysis. Different parametrizations of the structure functions areused. We discuss also mechanism with one forward $\Delta^+$ isobar, or otherproton resonances in the final state. The role of several cuts is studied. Wealso use SuperChic generator and compare corresponding results to the resultsof our codes. The soft rapidity gap survival factor is calculated for eachcontribution separately. The gap survival factor for the single-dissociativemechanism due to minijet emission into the main detector is calculated inaddition. It depends on the type of contribution (fully elastic, singledissociation, double dissociation). The soft rapidity gap survival factor forthe case of single proton measurement is significantly smaller than that forthe inclusive case (no proton measurement). We find only weak dependence on theinvariant mass of the dilepton system as well as the lepton pair transversemomentum and sizeable dependence on the pair rapidity. The latter effect israther difficult to identify experimentally.

Semiexclusive dilepton production in proton-proton collisions with one forward proton measurement at the LHC