Unitary coupled-channel three-body amplitude with pions and kaons
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, rearranging 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 𝑓 0 (500)(𝜎),𝑓 0 (980),𝜌(700),𝐾$^{*}_{0}$(700)(𝜅), and 𝐾*(892) resonances are included, apart from repulsive isobars. Different methods to evaluate the amplitude for physical momenta are discussed. Production amplitudes for 𝑎 1 quantum numbers are shown as a proof of principle for the numerical implementation.