The Form Factors of the Gauge-Invariant Three-Gluon Vertex

The gauge-invariant three-gluon vertex obtained from the pinch technique is characterized by thirteen nonzero form factors, which are given in complete generality for unbroken gauge theory at one loop. The results are given in $d$ dimensions using both dimensional regularization and dimensional reduction, including the effects of massless gluons and arbitrary representations of massive gauge bosons, fermions, and scalars. We find interesting relations between the functional forms of the contributions from gauge bosons, fermions, and scalars. These relations hold only for the gauge-invariant pinch technique vertex and are d-dimensional incarnations of supersymmetric nonrenormalization theorems which include finite terms. The form factors are shown to simplify for $N=1,2$, and 4 supersymmetry in various dimensions. In four-dimensional non-supersymmetric theories, eight of the form factors have the same functional form for massless gluons, quarks, and scalars, when written in a physically motivated tensor basis. For QCD, these include the tree-level tensor structure which has prefactor $\beta_0=(11N_c-2N_f)/3$, another tensor with prefactor $4N_c-N_f$, and six tensors with $N_c-N_f$. In perturbative calculations our results lead naturally to an effective coupling for the three-gluon vertex which depends on three momenta and gives rise to an effective scale which governs the behavior of the vertex. The effects of nonzero internal masses are important and have a complicated threshold and pseudo-threshold structure. The results of this paper are an important part of a gauge-invariant dressed skeleton expansion and a related multi-scale analytic renormalization scheme. In this approach the scale ambiguity problem is resolved since physical kinematic invariants determine the arguments of the couplings.Comment: 53 pages, 10 figures. v2: added reference

The Higgs Boson Mass in Split Supersymmetry at Two-Loops

The mass of the Higgs boson in the Split Supersymmetric Standard Model is calculated, including all one-loop threshold effects and the renormalization group evolution of the Higgs quartic coupling through two-loops. The two-loop corrections are very small (<<1 GeV), while the one-loop threshold corrections generally push the Higgs mass down several GeV.Comment: 17 pages. 4 figures. Improved discussion and notation. Corrected typos. Added references. Added plots. Main results unchange

Community as a Sustaining Force: Strategies for Online Scholarly Support

This paper discusses the ways that community connections serve to sustain and support scholarly growth, retention, and success, particularly in longer-term online contexts. These strategies are seen through the reflective experience of a faculty mentor and two recent graduates who co-developed community support strategies that help doctoral students stay motivated, connected, and succeed over many years of what might otherwise be a long, individual, and lonely journey—particularly when undertaken online. A matrix of strategies, apps, and online tools emerged from this process and is offered for consideration

The Physical Renormalization of Quantum Field Theories

The profound revolutions in particle physics likely to emerge from current and future experiments motivates an improved understanding of the precise predictions of the Standard Model and new physics models. Higher order predictions in quantum field theories inevitably requires the renormalization procedure, which makes sensible predictions out of the naively divergent results of perturbation theory. Thus, a robust understanding of renormalization is crucial for identifying and interpreting the possible discovery of new physics. The results of this thesis represent a broad set of investigations in to the nature of renormalization. The author begins by motivating a more physical approach to renormalization based on gauge-invariant Green's functions. The resulting effective charges are first applied to gauge coupling unification. This approach provides an elegant formalism for understanding all threshold corrections, and the gauge couplings unify in a more physical manner compared to the usual methods. Next, the gauge-invariant three-gluon vertex is studied in detail, revealing an interesting and rich structure. The effective coupling for the three-gluon vertex, {alpha}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}), depends on three momentum scales and gives rise to an effective scale Q{sub eff}{sup 2}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}) which governs the (sometimes surprising) behavior of the vertex. The effects of nonzero internal masses are important and have a complicated threshold and pseudo-threshold structure. The pinch-technique effective charge is also calculated to two-loops and several applications are discussed. The Higgs boson mass in Split Supersymmetry is calculated to two-loops, including all one-loop threshold effects, leading to a downward shift in the Higgs mass of a few GeV. Finally, the author discusses some ideas regarding the overall structure of perturbation theory. This thesis lays the foundation for a comprehensive multi-scale analytic renormalization scheme based on gauge-invariant Green's functions, in which the scale ambiguity problem is reduced since physical kinematic invariants determine the arguments of the couplings

Quantum Field Theory of Meson Mixing

We have developed a quantum field theoretic framework for scalar and pseudoscalar meson mixing and oscillations in time. The unitary inequivalence of the Fock space of base (unmixed) eigenstates and the physical mixed eigenstates is proven and shown to lead to a rich condensate structure. This is exploited to develop formulas for two flavor boson oscillations in systems of arbitrary boson occupation number. The mixing and oscillation can be understood in terms of vacuum condensate which interacts with the bare particles to induce non-trivial effects. We apply these formulas to analyze the mixing of $\eta$ with $\eta'$ and comment on the $K_L K_S$ system. In addition, we consider the mixing of boson coherent states, which may have future applications in the construction of meson lasers.Comment: 12 pages, 3 figures; Eqs.(10-12) corrected, leading to new physical insights; added paragraph under Eq.(24) explaining physical interpretation of mixing in terms of vacuum condensation; references added and minor typo correcte

Diagnostics for COVID-19: A case for field-deployable, rapid molecular tests for community surveillance

Across the globe, the outbreak of the COVID-19 pandemic is causing distress with governments doing everything in their power to contain the spread of the novel coronavirus (SARS-CoV-2) to prevent morbidity and mortality. Actions are being implemented to keep health care systems from being overstretched and to curb the outbreak. Any policy responses aimed at slowing down the spread of the virus and mitigating its immediate effects on health care systems require a firm basis of information about the absolute number of currently infected people, growth rates, and locations/hotspots of infections. The only way to obtain this base of information is by conducting numerous tests in a targeted way. Currently, in Ghana, there is a centralized testing approach, that takes 4-5 days for samples to be shipped and tested at central reference laboratories with results communicated to the district, regional and nationalstakeholders. This delay in diagnosis increases the risk of ongoing transmission in communities and vulnerable institutions. We have validated, evaluated and deployed an innovative diagnostic tool on a mobile laboratory platform to accelerate the COVID-19 testing. A preliminary result of 74 samples from COVID-19 suspected cases has a positivity rate of 12% with a turn-around time of fewer than 3 hours from sample taking to reporting of results, significantly reducing the waiting time from days to hours, enabling expedient response by the health system for contact tracing to reduce transmission and additionally improving case management

Renormalization-Scale-Invariant PQCD Predictions for R_e+e- and the Bjorken Sum Rule at Next-to-Leading Order

We discuss application of the physical QCD effective charge $\alpha_V$, defined via the heavy-quark potential, in perturbative calculations at next-to-leading order. When coupled with the Brodsky-Lepage-Mackenzie prescription for fixing the renormalization scales, the resulting series are automatically and naturally scale and scheme independent, and represent unambiguous predictions of perturbative QCD. We consider in detail such commensurate scale relations for the $e^+e^-$ annihilation ratio $R_{e^+e^-}$ and the Bjorken sum rule. In both cases the improved predictions are in excellent agreement with experiment.Comment: 13 Latex pages with 5 figures; to be published in Physical Review

Tetraspanin CD53 promotes lymphocyte recirculation by stablising L-selectin surface expression

Tetraspanins regulate key processes in immune cells; however, the function of the leukocyterestricted tetraspanin, CD53 has remained unknown. Here we show that CD53 is essential for lymphocyte recirculation. Lymph nodes of Cd53-/- mice were smaller than wild-type mice due to a marked reduction in B cells and a 50% decrease in T cells. This reduced cellularity reflected an inability of Cd53-/- B and T cells to efficiently home to lymph nodes, due to the near absence of L-selectin from Cd53-/- B cells and reduced stability of L-selectin on Cd53-/- T cells. Further analyses, including on human lymphocytes, showed that CD53 inhibits L-selectin shedding via both ADAM17-dependent and -independent mechanisms. The disruption in lymphocyte recirculation in Cd53-/- mice led to impaired immune responses dependent on antigen delivery to lymph nodes. Together these findings demonstrate a previously unrecognized essential role for CD53 in lymphocyte trafficking and immune responses