Status and Progress of Hamiltonian Effective Field Theory in Light Hadron Spectroscopy

Hadron resonances are intrinsically dynamical states whose observable properties are governed by the interplay between quark-model configurations and hadronic channels. Hamiltonian effective field theory provides a practical framework for connecting hadron dynamics with experimental observables and lattice QCD results. In this review, we outline the infinite- and finite-volume formulations of Hamiltonian effective field theory and survey its applications to light-hadron spectroscopy and resonance structure. By constraining the same Hamiltonian framework with experimental scattering data and lattice QCD spectra, Hamiltonian effective field theory can help distinguish among scenarios that describe the available scattering data comparably well. We further discuss the model uncertainties associated with the interpretation of resonance structure. We also review recent extensions of the Hamiltonian framework developed to address more complicated dynamical settings.