A dual model with a nonlinear proton Regge trajectory in the missing mass (M2X) channel is constructed. A background based on a direct-channel exotic trajectory, developed and applied earlier for the inclusive electron-proton cross section description in the nucleon resonance region, is used. The parameters of the model are determined from the extrapolations to earlier experiments. Predictions for the low-mass (2 < M2X < 8 GeV2) diffraction dissociation cross sections at the LHC energies are given.
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