We calculate for the first time cross sections for single and central diffractive as well as exclusive diffractive production of dilepton pairs in proton-proton collisions. Several differential distributions are shown. The inclusive diffractive processes are calculated using diffractive parton distributions extracted from the analysis of diffractive structure function and dijet production at HERA. We find that the inclusive single-diffractive Drell-Yan process is by about 2 orders of magnitude smaller than ordinary Drell-Yan process. The central-diffractive processes are smaller by one order of magnitude compared to single-diffractive ones. We consider also exclusive production of dilepton pairs. The exclusive photon-pomeron (pomeron-photon) process constitutes a background to the QED photon-photon process proposed to be used for controlling luminosity at LHC. Both processes are compared then in several differential distributions. We find a region of the phase space where the photon-pomeron or pomeron-photon contributions can be larger than the photon-photon one.Comment: 20 page, 19 figure
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