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 (βisobarsβ) of all isospins, πΌ = 0,1/2,1,3/2,2 , and it also allows for transitions within a given isobar. The π 0 β‘(500)β’(π),π 0 β‘(980),πβ‘(700),πΎ$^{*}_{0}$β‘(700)β’(π ), and πΎ*β‘(892) resonances are included, apart from repulsive isobars. Different methods to evaluate the amplitude for physical momenta are discussed. Production amplitudes for π 1 quantum numbers are shown as a proof of principle for the numerical implementation.