Multi-Hadron Scattering from Lattice Quantum Chromodynamics

This thesis develops lattice-QCD methods for studying hadron structure, scattering, and decays, with particular emphasis on multi-hadron resonances. The \texttt{Mathematica} package \texttt{OpTion} is developed to automate the construction of lattice multi-hadron operators. Finite-volume spectra are related to infinite-volume amplitudes through quantization conditions. For coupled-channel $D\pi$ scattering, the pion-mass dependence of the pole trajectories and the scattering length are determined, and the results support a two-pole structure for the $D_0^*(2300)$. The thesis then studies the three-pion decay of the $\omega(782)$. Two- and three-body spectra are calculated, and three-body quantization conditions and effective field theory descriptions are developed. The extracted resonance pole, extrapolated to the physical point, gives a mass and width consistent with experiment and establishes a practical first-principles procedure for interacting three-body systems. These methods are further applied to the $\pi(1300)$, providing, for the first time, first-principles predictions of its resonance pole at several pion masses and revealing significant three-body effects. Finally, radiative and semileptonic decays of charmed mesons are investigated, and a model-independent method is developed to extract transition form factors with improved precision. These results advance the first-principles study of coupled-channel and three-body hadron resonances and provide new insight into their structure and decays.