Construction of phenomenological ππ amplitudes

Abstract

We give a comprehensive description of our scheme for applying the Roy equations to ππ phenomenology. The method is applied to recent high statistics ππ experiments. The complete set of amplitudes consistent with these experiments and with the theoretical constraints of analyticity, crossing and unitarity are presented. We consider the implications of these results and discuss future experiments which could remove the final ambiguities in the low-energy ππ amplitude.