Production processes at extremely high energies

The production processes are identified that contribute to the rise of the total cross section in proton-proton scattering at extremely high energies, s->~. At such energies, the scattering can be described by a black disk (completely absorptive) with a radius expanding logarithmically with energy surrounded by a gray fringe (partially absorptive). For the leading term of (lns)^2 in the increasing total cross section, the gray fringe is neglected, and geometrical optics is generalized to production processes. It is known that half of the rise in the total cross section is due to elastic scattering. The other half is found to originate from the production of jets with relatively small momenta in the center-of-mass system.