High Energy Bounds from Low Energy Data

A method for deriving rigorous upper bounds on asymptotic values of total cross sections is discussed. The size of the bound is determined by low energy data. A functional form for the total cross section at high energies is assumed and bounds on the parameters introduced are obtained. The method is applied to 7r 7~ scattering, and numerical estimates, using experimental data, are given for different parametrizations. For an asymptotically constant (TV, wefind a,(“) 5 40 mb. Better data would improve the accuracy of this bound and could lower it significantly. (Submitted to The Physical Review) * Supported by the U. S. Atomic Energy Commission.