Theory of the coupled NN - πNN system

A review is presented of the current status of πNN theories that include the effect of pion absorption. We emphasize models that are unitary at the two and three-body level and that provide for a simultaneous description of all the processes NN → NN, NN → πNN, NN → πd, πd → πd and πd → πNN. Despite the availability of relatively sophisticated calculations, we conclude that none of the models are sufficiently accurate to make reliable predictions, and that at least a partial inclusion of four-body unitarity may be necessary.