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The rich structure of photon-exchange processes at hadron colliders isstudied. We discuss central vector meson production pp --> p + J/psi + p, Wproduction pp --> p + W + X and mu+ mu- production. Each process has distinct,and large, soft pp rescattering effects, which can be directly observed bydetecting the outgoing protons. This allows a probe of the optical density ofthe proton, which plays a crucial role in the evaluation of the rapidity gapsurvival probabilities in diffractive-like processes at hadron colliders. Wenote that an alternative mechanism for J/psi production is odderon, instead ofphoton, exchange; and that the ratio of odderon to photon contributions isenhanced (suppressed) for phi(Upsilon) vector meson production.Comment: 23 pages, 10 figures, Latex; some minor typos corrected, version to  appear in Eur.Phys.J.

Photon-exchange processes at hadron colliders as a probe of the dynamics of diffraction