The partial wave amplitude for high-energy pion-pion scattering

Abstract

An approximate solution to the N/ D equations is obtained in the high-energy region. The solution depends on the high-energy behaviour of N( v), on the inelasticity R( v) and on the partial wave dispersion integral over the left-hand cut. If one assumes that the diffraction picture correctly describes the high-energy dynamics, and if the function N( v) is sufficiently smooth at high energies, it is possible to obtain an integral equation for the inelasticity. Using the solution to this equation, the high-energy partial wave amplitude is then shown to depend only on the real part of the partial wave amplitude. The latter can be described approximately in terms of low-energy dynamics if the high-energy dynamics is peripheral. Thus, in this case, the unknown high-energy region can be determined in terms of the known low-energy region. If (as is indicated by some experimental data) the high-energy dynamics is central, the high-energy amplitude originates from a “bootstrap” mechanism.