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We discuss a phenomenological model that describes results on diffractive pp and pbar-p cross sections and event final states up to the Fermilab Tevatron collider energy of 1.96 TeV and use it to make predictions for Large Hadron Collider (LHC) collision energies up to 14 TeV and asymptotically as the pp collision energy goes to infinity. The model is anchored in a saturation effect observed in single diffraction dissociation that explains quantitatively the factorization breaking observed in soft and hard pp and pbar-p diffractive processes and in diffractive photoproduction and low Q-square deep inelastic scattering.

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