Particle Exchange Models in Three Body Systems

The phenomenological description of three body resonances is of considerable interest in hadron spectroscopy. States such as the X(3872) have been discovered to decay near thresholds of three hadrons, thus understanding their origin requires knowledge of three body effects. Three particle reactions can be parameterized within the isobar model, which contain rescattering effects. We consider the one-particle exchange (OPE) process, inherent to three body scattering systems, and investigate it's analytical properties. We discuss the singularity structure of the OPE processes, and how the rescattering effects can be constructed from their successive iterations.