Skewed Sudakov Regime, Harmonic Numbers, and Multiple Polylogarithms

On the example of massless QED we study an asymptotic of the vertex when only one of the two virtualities of the external fermions is sent to zero. We call this regime the skewed Sudakov regime. First, we show that the asymptotic is described with a single form factor, for which we derive a linear evolution equation. The linear operator involved in this equation has a discrete spectrum. Its eigenfunctions and eigenvalues are found. The spectrum is a shifted sequence of harmonic numbers. With the spectrum found, we represent the expansion of the asymptotic in the fine structure constant in terms of multiple polylogarithms. Using this representation, the exponentiation of the doubly logarithmic corrections of the Sudakov form factor is recovered. It is pointed out that the form factor of the skewed Sudakov regime is growing with the virtuality of a fermion decreasing at a fixed virtuality of another fermion.Comment: 6 page

The Challenge of Light-Front Quantisation: Recent Results

We explain what is the challenge of light-front quantisation, and how we can now answer it because of recent progress in solving the problem of zero modes in the case of non-Abelian gauge theories. We also give a description of the light-front Hamiltonian for SU(2) finite volume gluodynamics resulting from this recent solution to the problem of light-front zero modes.Comment: 17 pages, lecture delivered by GBP at the XXXIV PNPI Winter School, Repino, St.Petersburg, Russia, February 14-20, 2000, version to appear in the Proceeding

Phase composition, structure and properties of the spark plasma sintered ceramics obtained from the Al12Mg17-B-Si powder mixtures

In this work, composite materials were obtained by spark plasma sintering of an Al12Mg17-B-Si powder mixture. The structure, phase composition, and mechanical properties of the obtained composites were studied. It was found that various compounds based on B12 icosahedrons, such as AlB12, B4Si, and B6Si, are formed during spark plasma sintering. Based on the SEM images and results of XRD analysis of the obtained specimens, a probable scheme for the formation of the phase composition of composite materials during spark plasma sintering was proposed. An increase in the Al12Mg17-B powder content in the initial mixture from 30 to 70 wt% leads to an increase in hardness from 16.55 to 21.24 GPa and a decrease in the friction coefficient and wear rate from 0.56 to 0.32 and 13.60 to 5.60 10−5 mm−3/(N/m), respectively

Some New Results on Complex-Temperature Singularities in Potts Models on the Square Lattice

We report some new results on the complex-temperature (CT) singularities of $q$-state Potts models on the square lattice. We concentrate on the problematic region $Re(a) < 0$ (where $a=e^K$) in which CT zeros of the partition function are sensitive to finite lattice artifacts. From analyses of low-temperature series expansions for $3 \le q \le 8$, we establish the existence, in this region, of complex-conjugate CT singularities at which the magnetization and susceptibility diverge. From calculations of zeros of the partition function, we obtain evidence consistent with the inference that these singularities occur at endpoints $a_e, \ a_e^*$ of arcs protruding into the (complex-temperature extension of the) FM phase. Exponents for these singularities are determined; e.g., for $q=3$, we find $\beta_e=-0.125(1)$, consistent with $\beta_e=-1/8$. By duality, these results also imply associated arcs extending to the (CT extension of the) symmetric PM phase. Analytic expressions are suggested for the positions of some of these singularities; e.g., for $q=5$, our finding is consistent with the exact value $a_e,a_e^*=2(-1 \mp i)$. Further discussions of complex-temperature phase diagrams are given.Comment: 26 pages, latex, with eight epsf figure

Canonical Formulation of the Light-Front Gluodynamics and Quantization of the Non-Abelian Plane Waves

Without a gauge fixing, canonical variables for the light-front SU(2) gluodynamics are determined. The Gauss law is written in terms of the canonical variables. The system is qualified as a generalized dynamical system with first class constraints. Abeliazation is a specific feature of the formulation (most of the canonical variables transform nontrivially only under the action of an Abelian subgroup of the gauge transformations). At finite volume, a discrete spectrum of the light-front Hamiltonian $P_+$ is obtained in the sector of vanishing $P_-$. We obtain, therefore, a quantized form of the classical solutions previously known as non-Abelian plane waves. Then, considering the infinite volume limit, we find that the presence of the mass gap depends on the way the infinite volume limit is taken, which may suggest the presence of different ``phases'' of the infinite volume theory. We also check that the formulation obtained is in accord with the standard perturbation theory if the latter is taken in the covariant gauges.Comment: REVTEX, 18 pages, version to appear in Phys. Rev.

Complex-Temperature Singularities in the d=2d=2 Ising Model. III. Honeycomb Lattice

We study complex-temperature properties of the uniform and staggered susceptibilities $\chi$ and $\chi^{(a)}$ of the Ising model on the honeycomb lattice. From an analysis of low-temperature series expansions, we find evidence that $\chi$ and $\chi^{(a)}$ both have divergent singularities at the point $z=-1 \equiv z_{\ell}$ (where $z=e^{-2K}$), with exponents $\gamma_{\ell}'= \gamma_{\ell,a}'=5/2$. The critical amplitudes at this singularity are calculated. Using exact results, we extract the behaviour of the magnetisation $M$ and specific heat $C$ at complex-temperature singularities. We find that, in addition to its zero at the physical critical point, $M$ diverges at $z=-1$ with exponent $\beta_{\ell}=-1/4$, vanishes continuously at $z=\pm i$ with exponent $\beta_s=3/8$, and vanishes discontinuously elsewhere along the boundary of the complex-temperature ferromagnetic phase. $C$ diverges at $z=-1$ with exponent $\alpha_{\ell}'=2$ and at $v=\pm i/\sqrt{3}$ (where $v = \tanh K$) with exponent $\alpha_e=1$, and diverges logarithmically at $z=\pm i$. We find that the exponent relation $\alpha'+2\beta+\gamma'=2$ is violated at $z=-1$; the right-hand side is 4 rather than 2. The connections of these results with complex-temperature properties of the Ising model on the triangular lattice are discussed.Comment: 22 pages, latex, figures appended after the end of the text as a compressed, uuencoded postscript fil

Dark sectors 2016 Workshop: community report

This report, based on the Dark Sectors workshop at SLAC in April 2016, summarizes the scientific importance of searches for dark sector dark matter and forces at masses beneath the weak-scale, the status of this broad international field, the important milestones motivating future exploration, and promising experimental opportunities to reach these milestones over the next 5-10 years

Efficiency of Finding Muon Track Trigger Primitives in CMS Cathode Strip Chambers

In the CMS Experiment, muon detection in the forward direction is accomplished by cathode strip chambers~(CSC). These detectors identify muons, provide a fast muon trigger, and give a precise measurement of the muon trajectory. There are 468 six-plane CSCs in the system. The efficiency of finding muon trigger primitives (muon track segments) was studied using~36 CMS CSCs and cosmic ray muons during the Magnet Test and Cosmic Challenge~(MTCC) exercise conducted by the~CMS experiment in~2006. In contrast to earlier studies that used muon beams to illuminate a very small chamber area ($< \! 0.01$~m$^2$), results presented in this paper were obtained by many installed CSCs operating {\em in situ} over an area of $\approx \! 23$~m$^2$ as a part of the~CMS experiment. The efficiency of finding 2-dimensional trigger primitives within 6-layer chambers was found to be~$99.93 \pm 0.03\%$. These segments, found by the CSC electronics within $800$~ns after the passing of a muon through the chambers, are the input information for the Level-1 muon trigger and, also, are a necessary condition for chambers to be read out by the Data Acquisition System

A genetic cause of Alzheimer disease: mechanistic insights from Down syndrome

Down syndrome, caused by an extra copy of chromosome 21, is associated with a greatly increased risk of early onset Alzheimer disease. It is thought that this risk is conferred by the presence of three copies of the gene encoding amyloid precursor protein (APP), an Alzheimer risk factor, although the possession of extra copies of other chromosome 21 genes may also play a role. Further study of the mechanisms underlying the development of Alzheimer disease in Down syndrome could provide insights into the mechanisms that cause dementia in the general population