  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 two
often-used approximations to avoid the calculation of the three-body breakup
are not justified. The possible impact on pion production observables is
discussed.
