Beyond Color: Lattice Gauge Theory for Strongly-Coupled Physics
| Autor: | Oare, Patrick R. |
|---|---|
| Rok vydání: | 2024 |
| Druh dokumentu: | Diplomová práce |
| Popis: | Quantum Chromodynamics (QCD) is the prototypical strongly interacting Quantum Field Theory (QFT). It is the interaction that yields the strong nuclear force that binds protons and neutrons together. The underlying mathematical picture of QCD is known exactly: it is an 𝑆𝑈(3) gauge theory coupled to six flavors of fermions (the quarks). Despite this, it remains difficult to compute QCD observables because QCD is strongly-coupled, and typical perturbative methods used in QFT only work in specific regimes of validity for QCD. The most successful ab initio method to study QCD is Lattice Gauge Theory (LGT). This computational formalism computes observables by discretizing spacetime to render the path integral tractable. The primary focus of LGT in the 40 years since its inception has been the study of QCD, as the theory has direct physical relevance to so much of our universe, and the desire to understand QCD has driven many conceptual breakthroughs and advancements in LGT. Despite the focus on QCD, lattice methods find significant utility in studying other strongly-coupled gauge theories related to and unrelated to QCD. This thesis will focus on applying LGT to strongly-coupled physics inside and outside of QCD and on developing techniques within LGT that may be used to better understand said theories. First, the spectral function reconstruction problem in LGT is considered, and a new method for spectral function reconstruction in LGT is presented. Spectral functions describe the energy states of a theory: bound states, resonances, and continuum thresholds. The presented reconstruction method uses the analytic properties of the retarded Green’s function to constrain the full set of spectral functions that may be reconstructed from LGT data using the Nevanlinna-Pick interpolation problem. Next, two theories will be numerically studied using LGT. The first is the Standard Model Effective Field Theory (SMEFT). The SMEFT process that is considered is neutrinoless double 𝛽 (0𝜈𝛽𝛽) decay, a hypothetical decay of two neutrons into two protons and two electrons. LGT is used to compute non-perturbative matrix elements for the unphysical 𝜋⁻→ 𝜋⁺𝑒⁻𝑒⁻ transition, which contributes to nuclear 0𝜈𝛽𝛽 decay, and for the decay of the dinucleon 𝑛⁰𝑛⁰ → 𝑝⁺𝑝⁺𝑒⁻𝑒⁻. Connections to Effective Field Theory studies of 0𝜈𝛽𝛽 decay will also be discussed. Finally, adjoint QCD (QCD₂), the theory of a Majorana fermion coupled to a 𝑆𝑈(𝑁) gauge field in the adjoint representation in 1+1 spacetime dimensions, will be studied using LGT. QCD₂ is a well-studied QCD-like theory whose properties have been crucial in the study of confinement. Lattice methods are used to compute the static quark potential, string tensions, and the low-lying spectrum of the theory, which will provide input that may be used to understand better QCD₂ and the confinement mechanism in general. Ph.D. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
| Externí odkaz: |
|