Existence of Solutions of Crossing-SymmetricN/DEquations

Abstract

A fixed‐point theorem is applied to the N/D equations of ππ scattering, for which crossing is satisfied exactly by the absorptive part of the amplitude, up to a finite, but arbitrary cut off. It is found that ghost‐free solutions exist, if the subtraction constants are not too large, but that these solutions are not unique, since the Castillejo‐Dalitz‐Dyson ambiguity is not resolved by the requirement of crossing symmetry.