Single and double diffraction dissociation at the LHC is studied in a factorizable Regge-pole model, dominated by a Pomeron pole exchange in the t channel. While the contribution from secondary reggeon exchanges at the LHC is negligible, they are indispensable to match the lower-energy, ISR and FNAL data. To this end we append to the leading Pomeron exchange an effective reggeon. The main emphasis in our study is on the nucleon resonances in missing masses, that are accounted for by a dual model of the inelastic pP → M_X vertex, similar to the DIS structure function, known from HERA, with a non-linear nucleon, N~* trajectory in the direct, M_X~2 channel. Regge factorization and its breakdown due to a renormalization factor, tempering the energy rise is discussed.
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