Faddeev approach to pion production and pion-deuteron scattering

Some consequences of a new approach to pion production are explored in the threshold region. We treat the $\pi \mathrm{NN}$ system as a three-body system, with absorption (or production) occurring because of the existence of a $\pi N$ bound state in the $P_{11}$ (nucleon) channel. This description of the $\mathrm{NN}\pi$ vertex is justified by successfully using the model to calculate the long range part of the $N-N$ scattering amplitude. The results of the pion production calculation confirm a sensitivity to the short range behavior of the deuteron wave function and its $D$-state probability reported earlier. We also find a stronger variation of the production amplitude with energy than has previously been reported. This may resolve the apparent incompatibility of some experimental results. Finally, we also discuss the implications of the model for pion-deuteron elastic scattering.