In the last two decades, unexpected exotic resonances discovered in experiments challenged the quark model lore of hadrons. Tetraquarks, pentaquarks, molecules, hybrids, and glueball candidates sprung forth and revitalized the field of hadron spectroscopy. Many of those intriguing states decay into three or more particles. Due to non-trivial three-body couplings, determining their masses and widths requires some of the most complicated techniques on the border between lattice QCD and scattering theory. During the talk, I will review recent formal developments in this field, focusing on the importance of the analytic properties of the on-shell three-particle amplitudes. As an example, results from the studies of Efimov states, doubly-charmed tetraquark T_cc, and mixed systems of light mesons will be presented.
Whether we aim to test the fundamental symmetries of the standard model, or to understand the structure and reactions of nuclei or the equation of state of dense nuclear matter, it may be helpful or necessary to understand these phenomena starting from the underlying quarks and gluons which make up all known matter in the universe. After describing the complexities of this endeavor, I will highlight some recent progress and opportunities along this research direction.
