Toy model for pion production in nucleon-nucleon collisions. II. The role of three-particle singularities

The influence of three-particle breakup singularities on s-wave meson production in nucleon-nucleon collisions is studied within the distorted wave Born approximation. This study is based on a simple scalar model for the two-nucleon interaction and the production mechanism. An algorithm for the exact numerical treatment of the inherent three-body cuts, together with its straightforward implementation is presented. It is also shown that three often-used approximations to avoid the calculation of the three-body breakup are not justified. The possible impact on pion production observables is discussed.