The muon problem of flavor physics presents a rich opportunity to study beyond standard model physics. The as yet undiscovered bound state (μ+μ-), called true muonium, presents a unique opportunity to investigate the muon problem. The near-future experimental searches for true muonium will produce it relativistically, preventing the easy application of non-relativistic quantum mechanics. In this thesis, quantum field theory methods based on light-front quantization are used to solve an effective Hamiltonian for true muonium in the Fock space of |μ+μ-> , |μ+μ-γ> , |e+e->, |e+e-γ>, |τ+τ-> , and |τ+τ-γ> . To facilitate these calculations a new parallel code, True Muonium Solver With Front-Form Techniques (TMSWIFT), has been developed. Using this code, numerical results for the wave functions, energy levels, and decay constants of true muonium have been obtained for a range of coupling constants α. Work is also presented for deriving the effective interaction arising from the |γγ sector’s inclusion into the model.

With the discovery of the Higgs Boson in 2012, particle physics has decidedly moved beyond the Standard Model into a new epoch. Though the Standard Model particle content is now completely accounted for, there remain many theoretical issues about the structure of the theory in need of resolution. Among these is the hierarchy problem: since the renormalized Higgs mass receives quadratic corrections from a higher cutoff scale, what keeps the Higgs boson light? Many possible solutions to this problem have been advanced, such as supersymmetry, Randall-Sundrum models, or sub-millimeter corrections to gravity. One such solution has been advanced by the Lee-Wick Standard Model. In this theory, higher-derivative operators are added to the Lagrangian for each Standard Model field, which result in propagators that possess two physical poles and fall off more rapidly in the ultraviolet regime. It can be shown by an auxiliary field transformation that the higher-derivative theory is identical to positing a second, manifestly renormalizable theory in which new fields with opposite-sign kinetic and mass terms are found. These so-called Lee-Wick fields have opposite-sign propagators, and famously cancel off the quadratic divergences that plague the renormalized Higgs mass. The states in the Hilbert space corresponding to Lee-Wick particles have negative norm, and implications for causality and unitarity are examined.

This dissertation explores a variant of the theory called the N = 3 Lee-Wick

Standard Model. The Lagrangian of this theory features a yet-higher derivative operator, which produces a propagator with three physical poles and possesses even better high-energy behavior than the minimal Lee-Wick theory. An analogous auxiliary field transformation takes this higher-derivative theory into a renormalizable theory with states of alternating positive, negative, and positive norm. The phenomenology of this theory is examined in detail, with particular emphasis on the collider signatures of Lee-Wick particles, electroweak precision constraints on the masses that the new particles can take on, and scenarios in early-universe cosmology in which Lee-Wick particles can play a significant role.