The flavor symmetry in the standard model and the triality symmetry

A Dirac fermion is expressed by a 4 component spinor which is a combination of two quaternions and which can be treated as an octonion. The octonion possesses the triality symmetry, which defines symmetry of fermion spinors and bosonic vector fields. The triality symmetry relates three sets of spinors and two sets of vectors, which are transformed among themselves via transformations $G_{23}, G_{12}, G_{13}$, $G_{123}$ and $G_{132}$. If the electromagnetic (EM) interaction is sensitive to the triality symmetry, i.e. EM probe selects one triality sector, EM signals from the 5 transformed world would not be detected, and be treated as the dark matter. According to an astrophysical measurement, the ratio of the dark to ordinary matter in the universe as a whole is almost exactly 5. We expect quarks are insensitive to the triality, and triality will appear as three times larger flavor degrees of freedom in the lattice simulation.Comment: 16 pages 8 figures, To be published in International Journal of Modern Physics

Relativistic and Binding Energy Corrections to Direct Photon Production In Upsilon Decay

A systematic gauge-invariant method is used to calculate the rate for an upsilon meson to decay inclusively into a prompt photon. An expansion is made in the quark relative velocity v, which is a small natural parameter for heavy quark systems. Inclusion of these O(v^2) corrections tends to increase the photon rate in the middle z range and to lower it for larger z, a feature supported by the data.Comment: 13 pages, LateX, One figure (to be published in Phys. Rev. D, Sept. 1, 1996

Counting a black hole in Lorentzian product triangulations

We take a step toward a nonperturbative gravitational path integral for black-hole geometries by deriving an expression for the expansion rate of null geodesic congruences in the approach of causal dynamical triangulations. We propose to use the integrated expansion rate in building a quantum horizon finder in the sum over spacetime geometries. It takes the form of a counting formula for various types of discrete building blocks which differ in how they focus and defocus light rays. In the course of the derivation, we introduce the concept of a Lorentzian dynamical triangulation of product type, whose applicability goes beyond that of describing black-hole configurations.Comment: 42 pages, 11 figure

Algebraic properties of Gardner's deformations for integrable systems

An algebraic definition of Gardner's deformations for completely integrable bi-Hamiltonian evolutionary systems is formulated. The proposed approach extends the class of deformable equations and yields new integrable evolutionary and hyperbolic Liouville-type systems. An exactly solvable two-component extension of the Liouville equation is found.Comment: Proc. conf. "Nonlinear Physics: Theory and Experiment IV" (Gallipoli, 2006); Theor. Math. Phys. (2007) 151:3/152:1-2, 16p. (to appear

Colour-Octet Effects in Radiative Υ\Upsilon Decays

We investigate the effects of colour-octet contributions to the radiative $\Upsilon$ decay within the Bodwin, Braaten and Lepage NRQCD factorization framework. Photons coming both from the coupling to hard processes (`direct') and by collinear emission from light quarks (`fragmentation') are consistently included at next-to-leading order (NLO) in $\alpha_s$. An estimate for the non-perturbative matrix elements which enter in the final result is then obtained. By comparing the NRQCD prediction at NLO for total decay rates with the experimental data, it is found that the non-perturbative parameters must be smaller than expected from the na\"\i ve scaling rules of NRQCD. Nevertheless, colour-octet contributions to the shape of the photon spectrum turn out to be significant.Comment: 25 pages, Latex, 8 figure

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

Appointing Women to Boards: Is There a Cultural Bias?

Companies that are serious about corporate governance and business ethics are turning their attention to gender diversity at the most senior levels of business (Institute of Business Ethics, Business Ethics Briefing 21:1, 2011). Board gender diversity has been the subject of several studies carried out by international organizations such as Catalyst (Increasing gender diversity on boards: Current index of formal approaches, 2012), the World Economic Forum (Hausmann et al., The global gender gap report, 2010), and the European Board Diversity Analysis (Is it getting easier to find women on European boards? 2010). They all lead to reports confirming the overall relatively low proportion of women on boards and the slow pace at which more women are being appointed. Furthermore, the proportion of women on corporate boards varies much across countries. Based on institutional theory, this study hypothesizes and tests whether this variation can be attributed to differences in cultural settings across countries. Our analysis of the representation of women on boards for 32 countries during 2010 reveals that two cultural characteristics are indeed associated with the observed differences. We use the cultural dimensions proposed by Hofstede (Culture’s consequences: International differences in work-related values, 1980) to measure this construct. Results show that countries which have the greatest tolerance for inequalities in the distribution of power and those that tend to value the role of men generally exhibit lower representations of women on boards

Current Closure in the Auroral Ionosphere: Results from the Auroral Current and Electrodynamics Structure Rocket Mission

The Auroral Current and Electrodynamics Structure (ACES) mission consisted of two sounding rockets launched nearly simultaneously from Poker Flat Research Range, AK on January 29, 2009 into a dynamic multiple-arc aurora. The ACES rocket mission was designed to observe electrodynamic and plasma parameters above and within the current closure region of the auroral ionosphere. Two well instrumented payloads were flown along very similar magnetic field footprints, at different altitudes, with small temporal separation between both payloads. The higher altitude payload (apogee 360 km), obtained in-situ measurements of electrodynamic and plasma parameters above the current closure region to determine the input signature. The low altitude payload (apogee 130 km), made similar observations within the current closure region. Results are presented comparing observations of the electric fields, magnetic components, and the differential electron energy flux at magnetic footpoints common to both payloads. In situ data is compared to the ground based all-sky imager data, which presents the evolution of the auroral event as the payloads traversed through magnetically similar regions. Current measurements derived from the magnetometers on the high altitude payload observed upward and downward field-aligned currents. The effect of collisions with the neutral atmosphere is investigated to determine it is a significant mechanism to explain discrepancies in the low energy electron flux. The high altitude payload also observed time-dispersed arrivals in the electron flux and perturbations in the electric and magnetic field components, which are indicative of Alfven waves

alpha^2 corrections to parapositronium decay: a detailed description

We present details of our recent calculation of alpha^2 corrections to the parapositronium decay into two photons. These corrections are rather small and our final result for the parapositronium lifetime agrees well with the most recent measurement. Implications for orthopositronium decays are briefly discussed.Comment: 18 pages, late

Current Closure in the Auroral Ionosphere: Results from the Auroral Current and Electrodynamics Structure Rocket Mission

The Auroral Current and Electrodynamics Structure (ACES) mission consisted of two sounding rockets launched nearly simultaneously from Poker Flat Research Range, AK on January 29, 2009 into a dynamic multiple-arc aurora. The ACES rocket mission was designed to observe electrodynamic and plasma parameters above and within the current closure region of the auroral ionosphere. Two well instrumented payloads were flown along very similar magnetic field footprints, at different altitudes, with small temporal separation between both payloads. The higher altitude payload (apogee 360 km), obtained in-situ measurements of electrodynamic and plasma parameters above the current closure region to determine the input signature. The low altitude payload (apogee 130 km), made similar observations within the current closure region. Results are presented comparing observations of the electric fields, magnetic components, and the differential electron energy flux at magnetic footpoints common to both payloads. In situ data is compared to the ground based all-sky imager data, which presents the evolution of the auroral event as the payloads traversed through magnetically similar regions. Current measurements derived from the magnetometers on the high altitude payload observed upward and downward field-aligned currents. The effect of collisions with the neutral atmosphere is investigated to determine if it is a significant mechanism to explain discrepancies in the low energy electron flux. The high altitude payload also observed time-dispersed arrivals in the electron flux and perturbations in the electric and magnetic field components, which are indicative of Alfven waves