Three-body unitarity puts important constraints on the form of the scattering amplitudes required for the clarification of several puzzles in modern meson and baryon spectroscopy - e.g. Roper-puzzle, kinemaitic (triangle-) singularities in excited state of a1(1260), nature of XYZ states.
In my talk, I will demonstrate, how a minimal form of such a relativistic and unitary scattering amplitude can be derived and its recent applications. I will also discuss mathematical aspects and application to physical systems when applying such an amplitude to the finite-volume spectrum obtained from Lattice QCD.
[Eur.Phys.J. A53 (2017) no.9, 177]
[Eur.Phys.J. A53 (2017) no.12, 240]
[Phys.Rev.Lett. 122 (2019) no.6, 062503]