A simple model for elastic diffractive hadron scattering, reproducing the dip-bump structure is used to analyze pp andpp scattering. The main emphasis is on the delicate and non-trivial dynamics in the dip-bump region, near t = −1 GeV 2 . The simplicity of the model and the expected smallness of the absorption corrections enables one the control of various contributions to the scattering amplitude, in particular the interplay between the Ceven and C-odd components of the amplitude, as well as their relative contribution, changing with s and t. The role of the non-linearity of the Regge trajectories is scrutinized. The ratio of the real to imaginary parts of the forward amplitude, the ratio of elastic to total cross sections and the inelastic cross section are calculated. Predictions for the LHC energy region, where most of the exiting models will be either confirmed or ruled out, are presented.

A model for a Regge trajectory compatible with the threshold behavior required by unitarity and asymptotics in agreement with analyticity constraints is given in explicit form. The model is confronted in the time-like region with widths and masses of the mesonic resonances and, in the space-like region, the $\rho$ trajectory is compared with predictions derived from $\pi-N$ charge-exchange reaction. Breaking of the exchange degeneracy is studied in the model and its effect on both the masses and widths is determined.Comment: 17 pages, 3 figure

J= photoproduction is studied in the framework of the analytic S-matrix theory. The differential and integrated elastic cross sections for J= photoproduction are calculated from a dual amplitude with Mandelstam analyticity. It is argued that, at low energies, the background, which is the low-energy equivalent of the high-energy diffraction, replaces the Pomeron exchange. The onset of the high-energy Pomeron dominance is estimated from the fits to the data.