Lattice three-body problems in strange and charming hadrons

The hadron spectrum contains a rich variety of conventional and exotic states. Many of these states are unstable, and understanding their properties requires understanding how they scatter and decay. Three-body dynamics plays an essential role in this picture and presents a growing frontier for lattice QCD.

 

In this colloquium, I will discuss why three-body systems are challenging on the lattice and how their finite-volume spectra can be connected to physical scattering and decay processes. Three examples will illustrate different aspects of the problem: the $\omega(782)$ and its three-pion decay, the $\phi(1020)$ with coupled kaon--antikaon and three-pion channels, and the doubly charmed tetraquark $T_{cc}$, where the nearby $DD^*$ threshold and underlying $DD\pi$ dynamics are closely intertwined. Through these examples, I will discuss the challenges these systems pose for both lattice calculations and theoretical formalisms, and present our recent progress on both fronts.