Updated Analysis of an Unexpected Correlation Between Dark Matter and Galactic Ellipticity

We investigate a correlation between the dark matter content of elliptical galaxies and their ellipticity ϵ that was initially reported in 2014. We use new determinations of dark matter and ellipticities that are posterior to that time. Our data set consists of 237 elliptical galaxies passing a strict set of criteria that selects a homogeneous sample of typical elliptical galaxies. We find a relation between the mass-to-light ratio and ellipticity ϵ that is well fitted by M/L = (14.1 ± 5.4)ϵ, which agrees with the result reported in 2014. Our analysis includes 135 galaxies that were not in the 2014 analysis, and includes data sets with refined versions of previous methods. The consistency between the present and 2014 analyses reduces the possibility that the initial observation of the correlation came from approximations in the methods used to estimate dark matter content or lower resolution data, thereby lending support to a physical origin

QCD Running Couplings and Effective Charges

We discuss our present knowledge of $\alpha_s$, the fundamental running coupling or effective charge of Quantum Chromodynamics (QCD). A precise understanding of the running of $\alpha_s(Q^2)$ at high momentum transfer, $Q$, is necessary for any perturbative QCD calculation. Equally important, the behavior of $\alpha_s$ at low $Q^2$ in the nonperturbative QCD domain is critical for understanding strong interaction phenomena, including the emergence of mass and quark confinement. The behavior of $\alpha_s(Q^2)$ at all momentum transfers also provides a connection between perturbative and nonperturbative QCD phenomena, such as hadron spectroscopy and dynamics. We first sketch the origin of the QCD coupling, the reason why its magnitude depends on the scale at which hadronic phenomena are probed, and the resulting consequences for QCD phenomenology. We then summarize latest measurements in both the perturbative and nonperturbative domains. New theory developments include the derivation of the universal nonperturbative behavior of $\alpha_s(Q^2)$ from both the Dyson-Schwinger equations and light-front holography. We also describe theory advances for the calculation of gluon and quark Schwinger functions in the nonperturbative domain and the relation of these quantities to $\alpha_s$. We conclude by highlighting how the nonperturbative knowledge of $\alpha_s$ is now providing a parameter-free determination of hadron spectroscopy and structure, a central and long-sought goal of QCD studies.Comment: Invited review article, Prog Part. Nucl. Phys., in press. (143 pages, 9 figures

High precision determination of the Q2Q^2-evolution of the Bjorken Sum

We present a significantly improved determination of the Bjorken Sum for 0.6$\leq Q^{2}\leq$4.8 GeV$^{2}$ using precise new $g_{1}^{p}$ and $g_{1}^{d}$ data taken with the CLAS detector at Jefferson Lab. A higher-twist analysis of the $Q^{2}$-dependence of the Bjorken Sum yields the twist-4 coefficient $f_{2}^{p-n}=-0.064 \pm0.009\pm_{0.036}^{0.032}$. This leads to the color polarizabilities $\chi_{E}^{p-n}=-0.032\pm0.024$ and $\chi_{B}^{p-n}=0.032\pm0.013$. The strong force coupling is determined to be \alpha_{s}^{\overline{\mbox{ MS}}}(M_{Z}^{2})=0.1124\pm0.0061, which has an uncertainty a factor of 1.5 smaller than earlier estimates using polarized DIS data. This improvement makes the comparison between $\alpha_{s}$ extracted from polarized DIS and other techniques a valuable test of QCD.Comment: Published in Phys. Rev. D. V1: 8 pages, 3 figures. V2: Updated references; Included threshold matching in \alpha_s evolution. Corrected a typo on the uncertainty for \Lambda_QCD. V3: Published versio

Nonperturbative QCD Coupling and its β\beta function from Light-Front Holography

The light-front holographic mapping of classical gravity in AdS space, modified by a positive-sign dilaton background, leads to a nonperturbative effective coupling $\alpha_s^{AdS}(Q^2)$. It agrees with hadron physics data extracted from different observables, such as the effective charge defined by the Bjorken sum rule, as well as with the predictions of models with built-in confinement and lattice simulations. It also displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale $\sim 1$ GeV. The resulting $\beta$ function appears to capture the essential characteristics of the full $\beta$ function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD. Commensurate scale relations relate observables to each other without scheme or scale ambiguity. In this paper we extrapolate these relations to the nonperturbative domain, thus extending the range of predictions based on $\alpha_s^{AdS}(Q^2)$.Comment: 32 pages, 7 figures. Final version published in Phys. Rev.

Sum Rules and Moments of the Nucleon Spin Structure Functions

The nucleon has been used as a laboratory to investigate its own spin structure and Quantum Chromodynamics. New experimental data on nucleon spin structure at low to intermediate momentum transfers combined with existing high momentum transfer data offer a comprehensive picture of the transition region from the {\it confinement} regime of the theory to its {\it asymptotic freedom} regime. Insight for some aspects of the theory is gained by exploring lower moments of spin structure functions and their corresponding sum rules (i.e. the Gerasimov-Drell-Hearn, Bjorken and Burkhardt-Cottingham). These moments are expressed in terms of an operator product expansion using quark and gluon degrees of freedom at moderately large momentum transfers. The sum rules are verified to a good accuracy assuming that no singular behavior of the structure functions is present at very high excitation energies. The higher twist contributions have been examined through the moments evolution as the moments evolution as the momentum transfer varies from higher to lower values. Furthermore, QCD-inspired low-energy effective theories, which explicitly include chiral symmetry breaking, are tested at low momentum transfers. The validity of these theories is further examined as the momentum transfer increases to moderate values. It is found that chiral perturbation calculations agree reasonably well with the first moment of the spin structure function $g_1$ at momentum transfer of 0.1 GeV$^2$ but fail to reproduce the neutron data in the case of the generalized polarizability $\delta_{LT}$.Comment: 21 pages, 4 figures, review for Modern Physics Letters A. Minor modifications in text and improved quality for one figure. Corrected mistakes in section

Spin Sum Rules and the Strong Coupling Constant at large distance

We present recent results on the Bjorken and the generalized forward spin polarizability sum rules from Jefferson Lab Hall A and CLAS experiments, focusing on the low $Q^2$ part of the measurements. We then discuss the comparison of these results with Chiral Perturbation theory calculations. In the second part of this paper, we show how the Bjorken sum rule with its connection to the Gerasimov-Drell-Hearn sum, allows us to conveniently define an effective coupling for the strong force at all distances.Comment: Contribution to proceedings for the Workshop on Spin Structure at Long Distance (Newport News, March 2009

Analysis of Lean Premixed/Prevaporized Combustion with KIVA-2

Requirements to reduce the emissions of pollutants from gas turbines used in aircraft propulsion and ground based power generation have led to consideration of lean premixed/prevaporized (LPP) combustion concept. This paper describes some of the LPP flame tube analyses performed at the NASA Research Center with KIVA-2, a well-known multi-dimensional CFD code for problems including sprays, turbulence, and combustion. Modifications to KIVA-2's boundary condition and chemistry treatments have been made to meet the needs of the present study. The study itself focuses on two key aspects of the LPP concept, low emissions and flame stability (including flashback and lean blowoff

Roles of the color antisymmetric ghost propagator in the infrared QCD

The results of Coulomb gauge and Landau gauge lattice QCD simulation do not agree completely with continuum theory. There are indications that the ghost propagator in the infrared region is not purely color diagonal as in high energy region. After presenting lattice simulation of configurations produced with Kogut-Susskind fermion (MILC collaboration) and those with domain wall fermion (RBC/UKQCD collaboration), I investigate in triple gluon vertex and the ghost-gluon-ghost vertex how the square of the color antisymmetric ghost contributes. Then the effect of the vertex correction to the gluon propagator and the ghost propagator is investigated. Recent Dyson-Schwinger equation analysis suggests the ghost dressing function $G(0)=$ finite and no infrared enhancement or $\alpha_G=0$. But the ghost propagator renormalized by the loop containing a product of color antisymmetric ghost is expected to behave as $_r =-\frac{G(q^2)}{q^2}$ with $G(q^2)\propto q^{-2(1+\alpha_G)}$ with $\alpha_G = 0.5$, if the fixed point scenario is valid. I interpret the $\alpha_G=0$ solution should contain a vertex correction. The infrared exponent of our lattice Landau gauge gluon propagator of the RBC/UKQCD is $\kappa=\alpha_G=-0.5$ and that of MILC is about -0.7. The implication for the Kugo-Ojima color confinement criterion, QCD effective coupling and the Slavnov identity are given.Comment: 13 pages 10 figures, references added and revised. version to be published in Few-Body System