Quantifying Comparisons of Threshold Resummations

We explore similarities and differences between widely-used threshold resummation formalisms, employing electroweak boson production as an instructive example. Resummations based on both full QCD and soft-collinear effective theory (SCET) share common underlying factorizations and resulting evolution equations. The formalisms differ primarily in their choices of boundary conditions for evolution, in moment space for many treatments based on full QCD, and in momentum space for treatments based on soft-collinear effective theory. At the level of factorized hadronic cross sections, these choices lead to quite different expressions. Nevertheless, we can identify a natural expansion for parton luminosity functions, in which SCET and full QCD resummations agree for the first term, and for which subsequent terms provide differences that are small in most cases. We also clarify the roles of the non-leading resummation constants in the two formalisms, and observe a relationship of the QCD resummation function $D(\alpha_s)$ to the web expansion.Comment: 36 pages, 8 figure

A complete graphical calculus for Spekkens' toy bit theory

While quantum theory cannot be described by a local hidden variable model, it is nevertheless possible to construct such models that exhibit features commonly associated with quantum mechanics. These models are also used to explore the question of {\psi}-ontic versus {\psi}-epistemic theories for quantum mechanics. Spekkens' toy theory is one such model. It arises from classical probabilistic mechanics via a limit on the knowledge an observer may have about the state of a system. The toy theory for the simplest possible underlying system closely resembles stabilizer quantum mechanics, a fragment of quantum theory which is efficiently classically simulable but also non-local. Further analysis of the similarities and differences between those two theories can thus yield new insights into what distinguishes quantum theory from classical theories, and {\psi}-ontic from {\psi}-epistemic theories. In this paper, we develop a graphical language for Spekkens' toy theory. Graphical languages offer intuitive and rigorous formalisms for the analysis of quantum mechanics and similar theories. To compare quantum mechanics and a toy model, it is useful to have similar formalisms for both. We show that our language fully describes Spekkens' toy theory and in particular, that it is complete: meaning any equality that can be derived using other formalisms can also be derived entirely graphically. Our language is inspired by a similar graphical language for quantum mechanics called the ZX-calculus. Thus Spekkens' toy bit theory and stabilizer quantum mechanics can be analysed and compared using analogous graphical formalisms.Comment: Major revisions for v2. 22+7 page

Towards a Framework of Choices Made During the Lifecycles of Process Models

A variety of process modelling approaches exist. The tools provide visualizations and enable analyses of a process. However, analyses of a process depend fundamentally on the properties of the underlying process model. Choices that modellers make in building process models affect the quality of the created models and have an effect on what the models can be used for and can affect the process that is modelled. This paper reflects over the choices the processes modellers need to make in the course of building processes and proposes a framework to show how the choices are related to each other

CPT, T, and Lorentz Violation in Neutral-Meson Oscillations

Tests of CPT and Lorentz symmetry using neutral-meson oscillations are studied within a formalism that allows for indirect CPT and T violation of arbitrary size and is independent of phase conventions. The analysis is particularly appropriate for studies of CPT and T violation in oscillations of the heavy neutral mesons D, B_d, and B_s. The general Lorentz- and CPT-breaking standard-model extension is used to derive an expression for the parameter for CPT violation. It varies in a prescribed way with the magnitude and orientation of the meson momentum and consequently also with sidereal time. Decay probabilities are presented for both uncorrelated and correlated mesons, and some implications for experiments are discussed.Comment: 11 pages, references added, accepted in Physical Review