Minimal 3-to-3 Scattering Amplitudes

A relativistic K-matrix formalism is developed for a special class of elastic 3-to-3 amplitudes for which all 2-to-3 transitions are forbidden. The three-pion system and the isospin-3/2 state of three nucleons below the five-pion and pion production thresholds, respectively, are examples of this class. The primary result is a set of connected-kernel on-shell equations for computing unitary 3-to-3 amplitudes, following under the assumption of a minimal dynamics, which require only on-shell two-particle amplitudes as input. The latter model as well as the general formalism may provide a useful phenomenological framework for evaluating experimental results such as three-pion resonance formation.