Unified theory ofN−Nandπ−dscattering

Using a time ordered diagrammatic method, we derive a set of linear integral equations that couple the $N-N$ to the $\pi -d$ channel and satisfy two- and three-body unitarity. The resultant equations have dressed propagators for the nucleons, and dressed form factors for the $\pi \mathrm{NN}$ vertex. The inclusion of the full $\pi -N$ amplitude in the $P_{11}$ channel leads to a dressing of both the $\pi \mathrm{NN}$ vertex and $N-N$ propagator without changing the basic structure of the equations.