QCD and rising cross sections

We show that parton-parton scattering processes in QCD drive a rapid increase in the proton-proton scattering cross section at high energies, and use a diffraction-scattering formalism to obtain quantitative predictions for ${\sigma }_{\mathrm{tot}}$, ${\sigma }_{\mathrm{inel}}$, and ${\sigma }_{\mathrm{el}}$ at Superconducting Super Collider and cosmic-ray energies. We also predict a very rapid increase in the number of minijet events with √s .