Role of three-body unitarity inπ-N scattering

We consider the amplitude for \ensuremath{\pi}-N scattering within the framework of a Lagrangian of the form suggested by the cloudy bag model with volume coupling. By first exposing two-body, and then three-body unitarity, we derive a set of integral equations that couple the \ensuremath{\pi}N to the \ensuremath{\pi}\ensuremath{\pi}N channel. These equations satisfy two- and three-body unitarity, and can be used to describe \ensuremath{\pi}-N scattering both below and above the threshold for pion production. Below this threshold, the equations have the form of the Lippmann-Schwinger equation with the new feature that in the potential, the vertices in the pole diagram are undressed, while those in the crossed diagram are dressed. This feature allows for the proper description of the ${P}_{11}$ amplitude.