Upper Bounds for the Scattering Amplitude at High Energy

Abstract

Constraints imposed by unitarity and analyticity on the high-energy behavior of scattering amplitudes are studied in detail. The Froissart bound at nonforward (and nonbackward) angle is improved by two different methods: One is based on the analyticity in complex $cos\ensuremath{\theta}$ plane, and the other on the analyticity of the partial-wave amplitude in the complex angular-momentum plane. It is also shown that the Froissart bound at $\ensuremath{\theta}=0 or \ensuremath{\pi}$ cannot be improved insofar as one does not impose restrictions on the scattering amplitude other than unitarity and the analyticity in the $cos\ensuremath{\theta}$ plane. The scattering of particles with spin is discussed briefly.