
Heavy baryon chiral perturbation theory (HBChPT) to leading order provides a kernel to solve the BetheSalpeter equation for the P33 [Delta (1232)channel] pi N system, in the infinite nucleon mass limit. Crossed Born terms include, when iterated within the BetheSalpeter equation, both all one and some twopion intermediate states, hence preserving elastic unitarity below the twopion production threshold. This suggests searching for a solution with the help of dispersion relations and suitable subtraction constants, when all inelasticities are explicitly neglected. The solution allows for a successful description of the experimental phase shift from threshold Lip to roots = 1500 MeV in terms of four subtraction constants. Nexttoleading order HBChPT calculations are also used to estimate the unknown subtraction constants which appear in the solution. Large discrepancies are encountered which can be traced to the slow convergence rate of HBChPT.
