Phenomenology of high-momentum-transfer elastic processes

An analysis is carried out to extract the leading effective trajectories and residues in $\mathrm{pp}$ and ${\pi }^{-}p$ elastic scattering. The results are compared with the predictions of the constituent-interchange model and the logarithmic dual model, which are shown to be the only two types of theory capable of providing a uniform link between backward and forward Regge regions and the fixed-angle region. The hypothesis of a smooth connection between forward and backward Regge regions puts strong contraints on a priori unrelated trajectories and residues. The possibility of a connection between the two models is discussed. As expected from interchange theory the extracted ${\pi }^{-}p$ trajectory and residue behave quite differently than those for $\mathrm{pp}$. The dual model seems to give the best overall description of the $\mathrm{pp}$ trajectory and residue functions while the $\pi p$ results agree completely with the interchange predictions. The two model fits to $\mathrm{pp}$ elastic scattering at moderate energies (12-24 GeV) are used to extract an expected Pomeron term. The shape of the extracted diffractive contribution is strikingly similar to the recent CERN ISR differential cross sections which exhibit a dip at $t = -1.4\mathrm{}$ ${\mathrm{GeV}}^2$ and a slow falloff in the large-$t$ region.