High-Energy Cross Sections, Pomeranchuk Theorems, and Regge Poles

Following a proposal that the asymptotic behavior of the elastic scattering amplitude for any process is dominated by the Regge poles (J. Regge, Nuovo Cimento, 14: 951(1959); work is developed that prescribes minimum energies for the validity of the Pomeranchuk theorems (I. Ya. Pomeranchok, Soviet Phys.- JETP, 7: 499(1958); L. B. Okun and I. Ya. Pomeranchuk, Soviet Phys.-JETP, 3: 307(1956)), rates at which the cross sections are to approach a constant limit, and how the differences of particle-antiparticle cross sections are to approach zero. The pi /sup plus or minus cross sections are considered. (L.N.N.)