How imposing analyticity on a $\pi\pi$ phase shift analysis can reveal new solutions, explore experimental structures, and investigate the possibility of new resonances

Experiments on pi pi scattering determine only the modulus of the amplitude in the inelastic region. Fixed t and u analyticity in the form of conventional dispersion relations are used to determine the phase of the amplitude in this region. This analysis allows local structures in data to be isolated. The authors find alternative analytic unitary amplitudes exist equally well describing the CERN- Munich data on the pi /sup +/ pi /sup -/ channel. These amplitudes have quite different physical properties with different daughter resonances, which data on other channels and/or e/sup +/e/sup -/ annihilation will be able to distinguish in the very near future. (34 refs).