Electroweak three-hadron decays in a finite-volume

Developments in lattice QCD and finite-volume field theory are allowing the community to access non-perturbative few-hadron amplitudes from first principles QCD. One recent development is the framework to analyze three-hadron electroweak decays, for example K→3π weak decays, which maps the finite-volume electroweak matrix elements computable from lattice QCD to the corresponding infinite-volume decay amplitude. In this talk, I will present new non-trivial analytic and numerical studies of the finite- and infinite-volume framework for 1→3 decays in the presence of two- and three-body bound states. We recover the known Lellouch-Luscher framework in the appropriate two-body limit, and show that the decay coupling can be mapped to matrix element for a three-body bound state.