Nonperturbative aspects of the quark-photon vertex

The electromagnetic interaction with quarks is investigated through a relativistic, electromagnetic gauge-invariant treatment. Gluon dressing of the quark-photon vertex and the quark self-energy functions is described by the inhomogeneous Bethe-Salpeter equation in the ladder approximation and the Schwinger-Dyson equation in the rainbow approximation respectively. Results for the calculation of the quark-photon vertex are presented in both the time-like and space-like regions of photon momentum squared, however emphasis is placed on the space-like region relevant to electron scattering. The treatment presented here simultaneously addresses the role of dynamically generated $q\bar{q}$ vector bound states and the approach to asymptotic behavior. The resulting description is therefore applicable over the entire range of momentum transfers available in electron scattering experiments. Input parameters are limited to the model gluon two-point function, which is chosen to reflect confinement and asymptotic freedom, and are largely constrained by the obtained bound-state spectrum.Comment: 8 figures available on request by email, 25 pages, Revtex, DOE/ER/40561-131-INT94-00-5

Mesons as qbar-q Bound States from Euclidean 2-Point Correlators in the Bethe-Salpeter Approach

We investigate the 2-point correlation function for the vector current. The gluons provide dressings for both the quark self energy as well as the vector vertex function, which are described consistently by the rainbow Dyson-Schwinger equation and the inhomogeneous ladder Bethe-Salpeter equation. The form of the gluon propagator at low momenta is modeled by a 2-parameter ansatz fitting the weak pion decay constant. The quarks are confined in the sense that the quark propagator does not have a pole at timelike momenta. We determine the ground state mass in the vector channel from the Euclidean time Fourier transform of the correlator, which has an exponential falloff at large times. The ground state mass lies around 590 MeV and is almost independent of the model form for the gluon propagator. This method allows us to stay in Euclidean space and to avoid analytic continuation of the quark or gluon propagators into the timelike region.Comment: 21 pages (REVTEX), 8 Postscript figure

Nonperturbative Aspect of Axial Vector Vertex in the Global Color Symmetry Model

It is shown how the axial vector current of current quarks is related to that of constituent quarks within the framework of the global color symmetry model. Gluon dressing of the axial vector vertex and the quark self-energy functions is described by the inhomogeneous Bethe-Salpeter equation in the ladder approximation and the Schwinger-Dyson equation in the rainbow approximation, respectively.Comment: 10 page

Low-energy QCD: Chiral coefficients and the quark-quark interaction

A detailed investigation of the low-energy chiral expansion is presented within a model truncation of QCD. The truncation allows for a phenomenological description of the quark-quark interaction in a framework which maintains the global symmetries of QCD and permits a $1/N_c$ expansion. The model dependence of the chiral coefficients is tested for several forms of the quark-quark interaction by varying the form of the running coupling, $\alpha (q^2)$, in the infrared region. The pattern in the coefficients that arises at tree level is consistent with large $N_c$ QCD, and is related to the model truncation.Comment: 28 pages, Latex, 6 postscript figures available on request to [email protected]

In vivo imaging of brown adipose tissue vasculature reactivity during adrenergic stimulation of non-shivering thermogenesis in mice

Brown adipose tissue (BAT) is a fat tissue specialized in heat production (non-shivering thermogenesis) and used by mammals to defend core body temperature when exposed to cold. Several studies have shown that during non-shivering thermogenesis the increase in BAT oxygen demand is met by a local and specific increase in tissue’s blood flow. While the vasculature of BAT has been extensively studied postmortem in rodents using histology, optical and CT imaging techniques, vasculature changes during stimulation of non-shivering thermogenesis have never been directly detected in vivo. Here, by using computed tomography (CT) angiography with gold nanoparticles we investigate, non-invasively, changes in BAT vasculature during adrenergic stimulation of non-shivering thermogenesis by norepinephrine, a vasoconstrictor known to mediate brown fat heat production, and by CL 316,243, a specific β3-adrenergic agonist also known to elicit BAT thermogenesis in rodents. We found that while CL 316,243 causes local vasodilation in BAT, with little impact on the rest of the vasculature throughout the body, norepinephrine leads to local vasodilation in addition to peripheral vasoconstriction. As a result, a significantly greater relative increase in BAT perfusion is observed following the injection of NE compared to CL. This study demonstrates the use of in vivo CT angiography as an effective tool in assessing vascular reactivity in BAT both qualitatively and quantitatively in preclinical studies

Sharp Trace Hardy-Sobolev-Maz'ya Inequalities and the Fractional Laplacian

In this work we establish trace Hardy and trace Hardy-Sobolev-Maz'ya inequalities with best Hardy constants, for domains satisfying suitable geometric assumptions such as mean convexity or convexity. We then use them to produce fractional Hardy-Sobolev-Maz'ya inequalities with best Hardy constants for various fractional Laplacians. In the case where the domain is the half space our results cover the full range of the exponent $s \in (0,1)$ of the fractional Laplacians. We answer in particular an open problem raised by Frank and Seiringer \cite{FS}.Comment: 42 page

Nucleon form factors and a nonpointlike diquark

Nucleon form factors are calculated on q^2 in [0,3] GeV^2 using an Ansatz for the nucleon's Fadde'ev amplitude motivated by quark-diquark solutions of the relativistic Fadde'ev equation. Only the scalar diquark is retained, and it and the quark are confined. A good description of the data requires a nonpointlike diquark correlation with an electromagnetic radius of 0.8 r_pi. The composite, nonpointlike nature of the diquark is crucial. It provides for diquark-breakup terms that are of greater importance than the diquark photon absorption contribution.Comment: 5 pages, REVTEX, epsfig, 3 figure

Differences in [18F]FDG uptake in BAT of UCP1 −/− and UCP1 +/+ during adrenergic stimulation of non-shivering thermogenesis

Background: Brown adipose tissue (BAT) is a fat tissue found in most mammals that helps regulate energy balance and core body temperature through a sympathetic process known as non-shivering thermogenesis. BAT activity is commonly detected and quantified in [18F]FDG positron emission tomography/computed tomography (PET/CT) scans, and radiotracer uptake in BAT during adrenergic stimulation is often used as a surrogate measure for identifying thermogenic activity in the tissue. BAT thermogenesis is believed to be contingent upon the expression of the protein UCP1, but conflicting results have been reported in the literature concerning [18F]FDG uptake within BAT of mice with and without UCP1. Differences in animal handling techniques such as feeding status, type of anesthetic, type of BAT stimulation, and estrogen levels were identified as possible confounding variables for [18F]FDG uptake. In this study, we aimed to assess differences in BAT [18F]FDG uptake between wild-type and UCP1-knockout mice using a protocol that minimizes possible variations in BAT stimulation caused by different stress responses to mouse handling. Results: [18F]FDG PET/CT scans were run on mice that were anesthetized with pentobarbital after stimulation of non-shivering thermogenesis by norepinephrine. While in wild-type mice [18F]FDG uptake in BAT increased significantly with norepinephrine stimulation of BAT, there was no consistent change in [18F]FDG uptake in BAT of mice lacking UCP1. Conclusions: [18F]FDG uptake within adrenergically stimulated BAT of wild-type and UCP1-knockout mice can significantly vary such that an [18F]FDG uptake threshold cannot be used to differentiate wild-type from UCP1-knockout mice. However, while an increase in BAT [18F]FDG uptake during adrenergic stimulation is consistently observed in wild-type mice, in UCP1-knockout mice [18F]FDG uptake in BAT seems to be independent of β3-adrenergic stimulation of non-shivering thermogenesis

Survey of nucleon electromagnetic form factors

A dressed-quark core contribution to nucleon electromagnetic form factors is calculated. It is defined by the solution of a Poincare' covariant Faddeev equation in which dressed-quarks provide the elementary degree of freedom and correlations between them are expressed via diquarks. The nucleon-photon vertex involves a single parameter; i.e., a diquark charge radius. It is argued to be commensurate with the pion's charge radius. A comprehensive analysis and explanation of the form factors is built upon this foundation. A particular feature of the study is a separation of form factor contributions into those from different diagram types and correlation sectors, and subsequently a flavour separation for each of these. Amongst the extensive body of results that one could highlight are: r_1^{n,u}>r_1^{n,d}, owing to the presence of axial-vector quark-quark correlations; and for both the neutron and proton the ratio of Sachs electric and magnetic form factors possesses a zero.Comment: 43 pages, 17 figures, 12 tables, 5 appendice

Bregman Voronoi Diagrams: Properties, Algorithms and Applications

The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define many variants of Voronoi diagrams depending on the class of objects, the distance functions and the embedding space. In this paper, we investigate a framework for defining and building Voronoi diagrams for a broad class of distance functions called Bregman divergences. Bregman divergences include not only the traditional (squared) Euclidean distance but also various divergence measures based on entropic functions. Accordingly, Bregman Voronoi diagrams allow to define information-theoretic Voronoi diagrams in statistical parametric spaces based on the relative entropy of distributions. We define several types of Bregman diagrams, establish correspondences between those diagrams (using the Legendre transformation), and show how to compute them efficiently. We also introduce extensions of these diagrams, e.g. k-order and k-bag Bregman Voronoi diagrams, and introduce Bregman triangulations of a set of points and their connexion with Bregman Voronoi diagrams. We show that these triangulations capture many of the properties of the celebrated Delaunay triangulation. Finally, we give some applications of Bregman Voronoi diagrams which are of interest in the context of computational geometry and machine learning.Comment: Extend the proceedings abstract of SODA 2007 (46 pages, 15 figures