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On the nullification of threshold amplitudes

The nullification of threshold amplitudes is considered within the conventional framework of quantum field theory. The relevant Ward identities for the reduced theory are derived both on path-integral and diagrammatic levels. They are then used to prove the vanishing of tree-graph threshold amplitudes.Comment: 16 page

Normalization of QCD corrections in top quark decay

We discuss the effects of QCD corrections to the on-shell decay $t \to b W$. We resolve the scale ambiguity using the Brodsky-Lepage-Mackenzie scheme, and find that the appropriate coupling constant is $\alpha_{s}^{ \overline{MS}} (0.122m_{t})$. The largest long distance contribution comes from the definition of the on-shell mass of the top quark. We note that QCD corrections to the electroweak $\rho$ parameter are extremely small when the $\rho$ parameter is expressed in terms of the top quark width.Comment: 7 pages (LaTeX), TPI-MINN-94/16-T, UMN-TH-1252/9

Simulation and optimisation of terahertz emission from InGaAs and InP photoconductive switches

We simulate the terahertz emission from laterally-biased InGaAs and InP using a three-dimensional carrier dynamics model in order to optimise the semiconductor material. Incident pump-pulse parameters of current Ti:Sapphire and Er:fibre lasers are chosen, and the simulation models the semiconductor's bandstructure using parabolic Gamma, L and X valleys, and heavy holes. The emitted terahertz radiation is propagated within the semiconductor and into free space using a model based on the Drude-Lorentz dielectric function. As the InGaAs alloy approaches InAs an increase in the emitted power is observed, and this is attributed to a greater electron mobility. Additionally, low-temperature grown and ion-implanted InGaAs are modelled using a finite carrier trapping time. At sub-picosecond trapping times the terahertz bandwidth is found to increase significantly at the cost of a reduced emission power.Comment: 9 pages, 7 figure

E+ E- -> Tau+ Tau- at the Threshold and Beyond

The excitation curve for the $\tau^+ \, \tau^-$ production in electron positron annihilation near the threshold is revisited with the aim of updating and extending a previous work. We find that the corrections of the relative magnitude $O(\alpha)$ near the threshold are significantly contributed by the radiative modification of the Coulomb interaction between the $\tau$ leptons. The interpolation between the Coulomb effects at the threshold and the relativistic effects at higher energies is considered and the resulting formula is argued to have relative accuracy up to, but not including, terms of the order of $\alpha^2$ at any velocity of the $\tau$ leptons.Comment: 7 pages, 1 figure (LaTeX, figure appended in PostScript), UMN-TH-1232/93, TPI-MINN-93/61-

Testing refinements by refining tests

One of the potential benefits of formal methods is that they offer the possibility of reducing the costs of testing. A specification acts as both the benchmark against which any implementation is tested, and also as the means by which tests are generated. There has therefore been interest in developing test generation techniques from formal specifications, and a number of different methods have been derived for state based languages such as Z, B and VDM. However, in addition to deriving tests from a formal specification, we might wish to refine the specification further before its implementation. The purpose of this paper is to explore the relationship between testing and refinement. As our model for test generation we use a DNF partition analysis for operations written in Z, which produces a number of disjoint test cases for each operation. In this paper we discuss how the partition analysis of an operation alters upon refinement, and we develop techniques that allow us to refine abstract tests in order to generate test cases for a refinement. To do so we use (and extend existing) methods for calculating the weakest data refinement of a specification

On the Strong Coupling Limit of the Faddeev-Hopf Model

The variational calculus for the Faddeev-Hopf model on a general Riemannian domain, with general Kaehler target space, is studied in the strong coupling limit. In this limit, the model has key similarities with pure Yang-Mills theory, namely conformal invariance in dimension 4 and an infinite dimensional symmetry group. The first and second variation formulae are calculated and several examples of stable solutions are obtained. In particular, it is proved that all immersive solutions are stable. Topological lower energy bounds are found in dimensions 2 and 4. An explicit description of the spectral behaviour of the Hopf map S^3 -> S^2 is given, and a conjecture of Ward concerning the stability of this map in the full Faddeev-Hopf model is proved.Comment: 21 pages, 0 figure

The onset of e^+e^- -> tau^+ tau^- at threshold revisited

The precise knowledge of the onset of the cross section $\sigma(e^+e^- \to \tau^+\tau^-)$ at the threshold is necessary for improving the accuracy of determination of the $\tau$ mass from the threshold measurements. The QED radiative corrections of relative order $\alpha$ and $\alpha^2$, additional to the well known Coulomb factor, are considered in the threshold region. The correction terms of order $\alpha^2$ are calculated, which contain coefficients enhanced by large parameters. As a result it is argued that the known $O(\alpha)$ corrections provide the accuracy of the description of the cross section close to $10^{-4}$, rather than $10^{-3}$ as claimed in a recent literature. Also analytical expressions are provided for some limiting cases of the corrections, previously calculated numerically.Comment: 16 page