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Three-body dynamics above threshold is required for the reliable extraction of many amplitudes and resonances from experiment and lattice QCD. The S-matrix principle of unitarity can be used to construct dynamical coupled-channel approaches in which three particles scatter off each other, re-arranging two-body subsystems by particle exchange. This paper reports the development of a three-body coupled-channel, amplitude including pions and kaons. The unequal-mass amplitude contains two-body S- and P-wave subsystems ("isobars") of all isospins, I=0, \, 1/2, \, 1, \, 3/2, \, 2, and it also allows for transitions within a given isobar. The f₀ (500) \, (""), \, f₀ (980), \, (700), K₀^* (700) \, (""), and K^* (892) resonances are included, apart from repulsive isobars. Different methods to evaluate the amplitude for physical momenta are discussed. Production amplitudes for a₁ quantum numbers are shown as a proof of principle for the numerical implementation.
Feng et al. (Thu,) studied this question.