Picture-Hanging Puzzles

We show how to hang a picture by wrapping rope around n nails, making a polynomial number of twists, such that the picture falls whenever any k out of the n nails get removed, and the picture remains hanging when fewer than k nails get removed. This construction makes for some fun mathematical magic performances. More generally, we characterize the possible Boolean functions characterizing when the picture falls in terms of which nails get removed as all monotone Boolean functions. This construction requires an exponential number of twists in the worst case, but exponential complexity is almost always necessary for general functions.Comment: 18 pages, 8 figures, 11 puzzles. Journal version of FUN 2012 pape

Quaternion-Octonion SU(3) Flavor Symmetry

Starting with the quaternionic formulation of isospin SU(2) group, we have derived the relations for different components of isospin with quark states. Extending this formalism to the case of SU(3) group we have considered the theory of octonion variables. Accordingly, the octonion splitting of SU(3) group have been reconsidered and various commutation relations for SU(3) group and its shift operators are also derived and verified for different iso-spin multiplets i.e. I, U and V- spins. Keywords: SU(3), Quaternions, Octonions and Gell Mann matrices PACS NO: 11.30.Hv: Flavor symmetries; 12.10-Dm: Unified field theories and models of strong and electroweak interaction

Quaternion Octonion Reformulation of Quantum Chromodynamics

We have made an attempt to develop the quaternionic formulation of Yang - Mill's field equations and octonion reformulation of quantum chromo dynamics (QCD). Starting with the Lagrangian density, we have discussed the field equations of SU(2) and SU(3) gauge fields for both cases of global and local gauge symmetries. It has been shown that the three quaternion units explain the structure of Yang- Mill's field while the seven octonion units provide the consistent structure of SU(3)_{C} gauge symmetry of quantum chromo dynamics

Generalized Gravi-Electromagnetism

A self consistant and manifestly covariant theory for the dynamics of four charges (masses) (namely electric, magnetic, gravitational, Heavisidian) has been developed in simple, compact and consistent manner. Starting with an invariant Lagrangian density and its quaternionic representation, we have obtained the consistent field equation for the dynamics of four charges. It has been shown that the present reformulation reproduces the dynamics of individual charges (masses) in the absence of other charge (masses) as well as the generalized theory of dyons (gravito - dyons) in the absence gravito - dyons (dyons). key words: dyons, gravito - dyons, quaternion PACS NO: 14.80H

Octonion Quantum Chromodynamics

Starting with the usual definitions of octonions, an attempt has been made to establish the relations between octonion basis elements and Gell-Mann \lambda matrices of SU(3)symmetry on comparing the multiplication tables for Gell-Mann \lambda matrices of SU(3)symmetry and octonion basis elements. Consequently, the quantum chromo dynamics (QCD) has been reformulated and it is shown that the theory of strong interactions could be explained better in terms of non-associative octonion algebra. Further, the octonion automorphism group SU(3) has been suitably handled with split basis of octonion algebra showing that the SU(3)_{C}gauge theory of colored quarks carries two real gauge fields which are responsible for the existence of two gauge potentials respectively associated with electric charge and magnetic monopole and supports well the idea that the colored quarks are dyons

Magnetoluminescence

Pulsar Wind Nebulae, Blazars, Gamma Ray Bursts and Magnetars all contain regions where the electromagnetic energy density greatly exceeds the plasma energy density. These sources exhibit dramatic flaring activity where the electromagnetic energy distributed over large volumes, appears to be converted efficiently into high energy particles and gamma-rays. We call this general process magnetoluminescence. Global requirements on the underlying, extreme particle acceleration processes are described and the likely importance of relativistic beaming in enhancing the observed radiation from a flare is emphasized. Recent research on fluid descriptions of unstable electromagnetic configurations are summarized and progress on the associated kinetic simulations that are needed to account for the acceleration and radiation is discussed. Future observational, simulation and experimental opportunities are briefly summarized.Comment: To appear in "Jets and Winds in Pulsar Wind Nebulae, Gamma-ray Bursts and Blazars: Physics of Extreme Energy Release" of the Space Science Reviews serie

Search for single top quarks in the tau+jets channel using 4.8 fb−1^{-1} of ppˉp\bar{p} collision data

We present the first direct search for single top quark production using tau leptons. The search is based on 4.8 fb$^{-1}$ of integrated luminosity collected in $p\bar{p}$ collisions at $\sqrt{s}$=1.96 TeV with the D0 detector at the Fermilab Tevatron Collider. We select events with a final state including an isolated tau lepton, missing transverse energy, two or three jets, one or two of them $b$ tagged. We use a multivariate technique to discriminate signal from background. The number of events observed in data in this final state is consistent with the signal plus background expectation. We set in the tau+jets channel an upper limit on the single top quark cross section of \TauLimObs pb at the 95% C.L. This measurement allows a gain of 4% in expected sensitivity for the observation of single top production when combining it with electron+jets and muon+jets channels already published by the D0 collaboration with 2.3 fb$^{-1}$ of data. We measure a combined cross section of \SuperCombineXSall pb, which is the most precise measurement to date.Comment: 12 pages, 5 figure

Model-independent measurement of t\boldsymbol{t}-channel single top quark production in ppˉ\boldsymbol{p\bar{p}} collisions at s=1.96\boldsymbol{\sqrt{s}=1.96} TeV

We present a model-independent measurement of $t$-channel electroweak production of single top quarks in \ppbar collisions at $\sqrt{s}=1.96\;\rm TeV$. Using $5.4\;\rm fb^{-1}$ of integrated luminosity collected by the D0 detector at the Fermilab Tevatron Collider, and selecting events containing an isolated electron or muon, missing transverse energy and one or two jets originating from the fragmentation of $b$ quarks, we measure a cross section \sigma({\ppbar}{\rargap}tqb+X) = 2.90 \pm 0.59\;\rm (stat+syst)\; pb for a top quark mass of $172.5\;\rm GeV$. The probability of the background to fluctuate and produce a signal as large as the one observed is $1.6\times10^{-8}$, corresponding to a significance of 5.5 standard deviations.Comment: 8 pages, 4 figures, submitted to Phys. Lett.

Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model

We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGO's second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h095%=3.47×10-25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering. © 2019 American Physical Society

Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background

The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy densities of tensor, vector, and scalar modes at 95% credibility to Ω0T<5.58×10-8, Ω0V<6.35×10-8, and Ω0S<1.08×10-7 at a reference frequency f0=25 Hz. © 2018 American Physical Society