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The diffractive production of vector mesons in deep inelastic scattering(DIS) is calculated in the McLerran-Venugopalan model. This is relevant whenlarge parton densities are probed by the virtual photon, as is the case atsmall Bjorken x or in DIS off nuclei. We investigate differences between theexclusive production (when the target doesn't break up) which dominates atsmall momentum transfer squared |t|, and the diffractive production (when thetarget scatters inelastically) which dominates at large |t|.

Exclusive vs. diffractive vector meson production in DIS at small x or off nuclei