Symmetrization of Relativistic Three-Body Partial Wave Amplitudes

Among the many challenges in predicting properties of hadrons from QCD is the modeling of interactions involving three or more particles. Three body effects are critical to studies of exotic hadrons like the π₁ and the T_cc, which have been observed to decay into three-body final states. Resonances like the π₁ will appear in partial wave projections of 3π→3π scattering amplitudes, but recent descriptions of these amplitudes from S-matrix theory are incomplete and rely on an asymmetric choice of basis. We present a symmetrized form of a 3→3 reaction amplitude that has this unphysical basis dependence removed, and we demonstrate the validity of our result with a numerical application of our symmetrization procedure to a toy model three-pion process. We visualize this system with Dalitz plots that exhibit the rich symmetry features which are anticipated of three-pion interactions. The Dalitz plots we present are one example of many observables one could construct using our symmetrized amplitude to predict features of hadronic interactions from QCD.