| Summary: | The Standard Model of particle physics provides a beautiful description of our universe at the most fundamental level and has been tested more thoroughly than any other scientific theory in history. Nevertheless, there are still unanswered questions lying at the frontiers of the Standard Model, ranging from composite structure formation to the violation of symmetries to the nature of the elusive neutrino. Answering these questions requires relating experimentally relevant hadrons to the fundamental Standard Model interactions of the quarks and gluons that compose them, made difficult by the fact that quantum chromodynamics is non-perturbative at low energies. In the face of the breakdown of perturbation theory, lattice QCD – a discretization of the Feynman path integral on a four-dimensional space-time grid – is the only known method for studying quarks and gluons at the energies relevant for hadron formation and structure.
This thesis will use lattice QCD to investigate the proton charge radius, CP violation, and neutrinoless double-beta decay. The electric charge radius of the proton, relevant for electronic scattering and for hydrogen spectroscopy, has historically been a subject of debate due to conflicting experimental measurements. This work performed an exploratory lattice QCD calculation of this charge radius directly from the dynamics of quarks and gluons constituting the proton using a novel method designed to reduce a systematic uncertainty that had plagued many previous calculations. CP symmetry, the combination of charge conjugation and parity, is violated in rare quark decays, and isolating the CP-violating phase δ in the quark sector of the Standard Model requires a theoretical understanding of the initial and final hadronic states involved in the decays. The light-cone distribution amplitude of the pion computed in this work from lattice QCD is one of the theoretical inputs required to extract δ from B --> ππ decays. The quest to resolving whether the neutrino is Majorana or Dirac has led to experimental searches for neutrinoless double-beta decay, but interpretations of experimental results depend on nuclear matrix elements of the isotopes in question. This work describes the first exploratory lattice QCD calculation of this nuclear matrix element for the nn --> ppee transition. In all these cases, lattice QCD provides the necessary theoretical input to understand experimentally relevant physics directly from the fundamental interactions of the Standard Model, advancing the frontiers of our understanding of the universe.
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