A unitary coupled-channel three-body amplitude with pions and kaons

We construct a dynamical coupled-channel model in which three particles scatter off each other based on the unitarity of the S-matrix. Multiple channels are included by re-arranging two-body subsystems (“isobars”) by particle exchange, with the third particle being the “spectator”. Spectator pions and kaons with unequal masses are inculded to analyze scattering processes including axial quantum numbers. Two-body subsystems up to P-wave are incorporated into our model of isospins: I=0, 1/2, 1, 3/2, 2. The analysis of production process requires the analytic continuation to real momenta. Different methods are discussed, including path deformation and continued fractions. A triangle singularity (TS) has also been observed in the production amplitude, which arises from intermediate decays due to three-body effects, which mimics the a₁(1420) resonance. Our coupled-channel framework is extendable to other quantum numbers, which enables us to to study dynamical resonance generation, and exotic channels, and lattice QCD data is being prepared for us to fit to experimental data.