Decays of polarized top quarks to lepton, neutrino and jets at NLO QCD

We compute the differential and total rate of the semileptonic decay of polarized top-quarks $t\to \ell \nu_\ell + b{\rm jet} + {\rm jet}$ at next-to-leading order (NLO) in the QCD coupling with an off-shell intermediate $W$ boson. We present several normalized distributions, in particular those that reflect the $t$-spin analyzing powers of the lepton, the b-jet and the $W^+$ boson at LO and NLO QCD.Comment: Latex, 22 page

The Determination of the Strong Coupling Constant

The strong coupling constant is one of the fundamental parameters of the standard model of particle physics. In this review I will briefly summarise the theoretical framework, within which the strong coupling constant is defined and how it is connected to measurable observables. Then I will give an historical overview of its experimental determinations and discuss the current status and world average value. Among the many different techniques used to determine this coupling constant in the context of quantum chromodynamics, I will focus in particular on a number of measurements carried out at the Large Electron Positron Collider (LEP) and the Large Hadron Collider (LHC) at CERN.Comment: A contribution to: The Standard Theory up to the Higgs discovery - 60 years of CERN, L. Maiani and G. Rolandi, ed

Drivers and potential predictability of summer time North Atlantic polar front jet variability

The variability of the North Atlantic polar front jet stream is crucial in determining summer weather around the North Atlantic basin. Recent extreme summers in western Europe and North America have highlighted the need for greater understanding of this variability, in order to aid seasonal forecasting and mitigate societal, environmental and economic impacts. Here we find that simple linear regression and composite models based on a few predictable factors are able to explain up to 40% of summertime jet stream speed and latitude variability from 1955 onwards. Regression models covering the earlier part of the twentieth century are much less effective, presumably due to decreased availability of data, and increased uncertainty in observational reanalyses. Sea surface temperature (SST) forcings impact predominantly on jet speed, whereas solar and cryospheric forcings appear to influence jet latitude. The cryospheric associations come from the previous autumn, suggesting the survival of an ice-induced signal through the winter season, whereas solar influences lead jet variability by a few years. Wavelet coherence analysis identifies that associations fluctuate over the study period but it is not clear whether this is just internal variability or actual non-stationarity. Finally we identify areas for future research

Moduli spaces for finite-order jets of Riemannian metrics

We construct the moduli space of r-jets at a point of Riemannian metrics on a smooth manifold. The construction is closely related to the problem of classification of jet metrics via differential invariants. The moduli space is proved to be a differentiable space which admits a finite canonical stratification into smooth manifolds. A complete study on the stratification of moduli spaces is carried out for metrics in dimension n=2.Comment: 25 pages, corrected typos, partially changed content with an appendix adde

Classifying singularities up to analytic extensions of scalars is smooth

AbstractThe singularity space consists of all germs (X,x), with X a Noetherian scheme and x a point, where we identify two such germs if they become the same after an analytic extension of scalars. This is a complete, separable space for the metric given by the order to which jets (=infinitesimal neighborhoods) agree after base change. In the terminology of descriptive set-theory, the classification of singularities up to analytic extensions of scalars is a smooth problem. Over C, the following two classification problems up to isomorphism are then also smooth: (i) analytic germs; and (ii) polarized schemes

The Atlas Structure of Images

Many operations of vision require image regions to be isolated and inter-related. This is challenging when they are different in detail and extent. Practical methods of Computer Vision approach this through the tools of downsampling, pyramids, cropping and patches. In this paper we develop an ideal geometric structure for this, compatible with the existing scale space model of image measurement. Its elements are apertures which view the image like fuzzy-edged portholes of frosted glass. We establish containment and cause/effect relations between apertures, and show that these link them into cross-scale atlases. Atlases formed of Gaussian apertures are shown to be a continuous version of the image pyramid used in Computer Vision, and allow various types of image description to naturally be expressed within their framework. We show that views through Gaussian apertures are approximately equivalent to the jets of derivative of Gaussian filter responses that form part of standard Scale Space theory. This supports a view of the simple cells of mammalian V1 as implementing a system of local views of the retinal image of varying extent and resolution. As a worked example we develop a keypoint descriptor scheme that outperforms previous schemes that do not make use of learning