Unitarity and High-Energy Behavior of Scattering Amplitudes

Upper and lower bounds of the imaginary part of a scattering amplitude are obtained for physical and unphysical values of the scattering angle, respectively, from unitarity alone. This imposes rather stringent conditions on the high-energy behavior of the scattering amplitude. In particular unitarity alone rules out Regge poles with value larger than unity for zero momentum transfer. On the other hand, it is shown that the total cross section cannot increase faster than the logarithm squared of the energy under assumptions appreciably more general than Mandelstam representation. Finally, in the light of the preceding results, we give a few comments on the problem of the shrinking of the diffraction peak and its connection with the decrease of the elastic cross section.