Increasing Cross Sections, Diffractive Excitation, and the Triple-Pomeron Coupling

Using model-independent sum rules, it is argued that the sharp peak near the kinematical boundary observed in some inclusive spectra and the increase of total cross sections are due to the same mechanism. Both phenomena are quantitatively described in proton-proton scattering, in terms of diffractive excitation into high-mass states with a triple-Pomeron coupling. This coupling is then incorporated in a two-component model. In this way we obtain a total inelastic proton-proton cross section which agrees with the data from $s=30\mathrm{} \mathrm{to} 3000$ Ge${\mathrm{V}}^2$. The "break" in the elastic differential cross section at small $\mathrm{}\left|t\right|\mathrm{}$ is related to the increase with energy of the inelastic cross section. Predictions, based on the factorizability of the Pomeron, are given for the inclusive spectra, inelastic and elastic cross sections, at Serpukhov and National Accelerator Laboratory energies, for $K^{+}p$ and other reactions. It is shown that a Pomeron with intercept slightly below unity can actually give rise to an increasing cross section and also that a perturbative approach to the Pomeron coupling with only the first few terms may be sufficient at and even far beyond CERN Intersecting Storage Rings energies, while the "true" asymptotic behavior appears only much later.