A new type of disconnectedness problem in a field-theory model of the NNπ system

When treated as an effective three-body problem in the framework of a simple field-theory model, the NNπ system acquires, in addition to the disconnected subsystem interactions usually considered, a new type of disconnected driving term, possible only for non-conserved particles such as the π. These terms pose a disconnectedness problem more intricate than that solved by Faddeev's equations or their known modifications for connected three-body forces. The solution of this problem in terms of a set of connected-kernel integral equations is presented.