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**Finite-Volume Methods in Hadron Spectroscopy with Lattice QCD and EFT**

One of the overarching goals in nuclear physics is to rigorously compute properties of hadronic systems directly from the fundamental theory of the strong interaction, Quantum Chromodynamics (QCD). Reliable calculations of nuclear processes are vital to the understanding of physical phenomena at various energy scales, including big bang nucleosynthesis and experimental searches for neutrinoless double beta decay, but the non-perturbative nature of QCD has restricted ab-initio calculations. Lattice QCD (LQCD) is currently the only reliable non-perturbative option for calculations of low-energy nuclear observables and has advanced in the last decade to study past stable bound states of QCD toward resonances and exotic states. LQCD calculations are performed in a finite Euclidean spacetime, requiring formalism to map the finite-volume (FV) observables calculated on the lattice to infinite-volume physical quantities. Advances in LQCD algorithms and FV formalisms have allowed LQCD to study few-body hadronic observables that include elastic/inelastic cross sections and transition form factors of both mesonic and Baryonic scattering systems. These developments are part of a larger goal to provide a quantitative description of the resonant nuclear spectrum and resolve puzzles that obscure our current understanding of QCD. This thesis will focus on the application and extension of the FV formalism toward the spectroscopic study of hadrons using scattering theory and lattice methods:

1. The extraction of scattering amplitudes of the Lambda (1405) resonance as a first-principles determination of a coupled-channel meson-baryon scattering system

2. the determination of scattering phases and partial-wave mixing angles for the deuteron and dineutron channels in the two-nucleon (baryon-baryon scattering) sector at the SU(3) symmetric point

3. the first application of the FV formalism to extract matrix elements of 2+J -> 2 (coupling two-hadron states via an external current) transition amplitudes from the lattice using a non-relativistic lattice effective field theory (EFT) for proton-neutron scattering with an electromagnetic current at low energies.