Multi-Particle Spectroscopy and Structure from Lattice Quantum Field Theory

A central goal of nuclear physics is the rigorous computation of hadronic properties directly from Quantum Chromodynamics (QCD), the fundamental theory of the strong interaction. Such calculations are essential for understanding physical phenomena across a wide range of energy scales, from big bang nucleosynthesis and neutrino-nucleus interactions to experimental searches for neutrinoless double beta decay. However, the inherently non-perturbative nature of QCD at low energies has long hindered truly ab-initio approaches. Lattice QCD has emerged as a systematically improvable framework capable of addressing this challenge, enabling first-principles calculations of low-energy nuclear observables and, more recently, the properties of short-lived hadronic resonances. This dissertation presents a series of studies employing lattice field theory methods to investigate the low-energy nuclear spectrum and to develop reliable techniques for extracting structural information of composite hadronic states via matrix elements. First, the first coupled-channel lattice QCD study of meson-baryon scattering is presented, focusing on the $\pi \Sigma$-$\bar{K}N$ coupled system to provide a rigorous first-principles explanation of the $\Lambda(1405)$ resonance. Second, a high-statistics investigation of nucleon-nucleon ($NN$) scattering is described, from which scattering phase shifts are extracted for both the deuteron and dineutron channels. Finally, a non-perturbative lattice effective field theory calculation of the deuteron electromagnetic form factor is presented, demonstrating a path toward extracting structural observables of light nuclei from the underlying theory.