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The strong running coupling from an approximate gluon Dyson-Schwinger equation

Description: Using Mandelstam`s approximation to the gluon Dyson-Schwinger equation we calculate the gluon self-energy in a renormalisation group invariant fashion. We obtain a non-perturbative {Beta} function. The scaling behavior near the ultraviolet stable fixed point is in good agreement with perturbative QCD. No further fixed point for positive values of the coupling is found: {alpha}{sub S} increases without bound in the infrared.
Date: October 1, 1996
Creator: Alkofer, R.; Hauck, A. & Von Smekal, L.
Partner: UNT Libraries Government Documents Department

Discrete anomaly and dynamical mass in 2+1 dimension U(1){sub v} {times} U(1){sub A} model

Description: The authors note that in (2+1)-dimensional gauge theories with even number of massless fermions, there is anomalous Z{sub 2} symmetry if theory is regularized in a parity-invariant way. They then consider a parity invariant U(1){sub v} {times} U(1){sub A} model, which induces a mutual Chern-Simons term in the effective action due to Z{sub 2} anomaly. The effect of the discrete anomaly is studied in the induced spin and in the dynamical fermion mass.
Date: December 31, 1995
Creator: Hong, D.K.
Partner: UNT Libraries Government Documents Department

Non-equilibrium QCD of high-energy multi-gluon dynamics

Description: A non-equilibrium QCD description of multiparticle dynamics in space-time is of both fundamental and phenomenological interest. Here the authors discusses an attempt to derive from first principles, a real-time formalism to study the dynamical interplay of quantum and statistical-kinetic properties of non-equilibrium multi-parton systems produced in high-energy QCD processes. The ultimate goal (from which one is still far away) is to have a practically applicable description of the space-time evolution of a general initial system of gluons and quarks, characterized by some large energy or momentum scale, that expands, diffuses and dissipates according to the self- and mutual-interactions, and eventually converts dynamically into final state hadrons. For example, the evolution of parton showers in the mechanism of parton-hadron conversion in high-energy hadronic collisions, or, the description of formation, evolution and freezeout of a quark-gluon plasma, in ultra-relativistic heavy-ion collisions.
Date: December 31, 1996
Creator: Geiger, K.
Partner: UNT Libraries Government Documents Department

A continuum order parameter for deconfinement

Description: Dyson-Schwinger equations are presented as a non-perturbative tool for the study and modeling of QCD at finite-{ital T}. An order parameter for deconfinement, applicable for both light and heavy quarks, is introduced. In a simple Dyson-Schwinger equation model of two-flavor QCD, coincident, 2nd-order chiral symmetry restoration and deconfinement transitions occur at {ital T} {approx} 150 MeV, with the same critical exponent, {Beta} {approx} 0.33.
Date: March 1, 1997
Creator: Roberts, C.D.
Partner: UNT Libraries Government Documents Department

Temperature, chemical potential and the {rho}-meson

Description: Models of QCD must confront nonperturbative phenomena such as confinement, dynamical chiral symmetry breaking (DCSB) and the formation of bound states. In addition, a unified approach should describe the deconfinement and chiral symmetry restoring phase transition exhibited by strongly-interacting matter under extreme conditions of temperature and density. Nonperturbative Dyson-Schwinger equation (DSE) models provide insight into a wide range of zero temperature hadronic phenomena; e.g., non-hadronic electroweak interactions of light- and heavy-mesons, and diverse meson-meson and meson-nucleon form factors. This is the foundation for their application at nonzero-(T, {mu}). Herein the authors describe the calculation of the reconfinement and chiral symmetry restoring phase boundary, and the medium dependence of {rho}-meson properties. They also introduce an extension to describe the time-evolution in the plasma of the quark's scalar and vector self energies based on a Vlasov equation.
Date: February 17, 2000
Creator: Roberts, C. D. & Schmidt, S. M.
Partner: UNT Libraries Government Documents Department

Vertex Sensitivity in the Schwinger-Dyson Equations of QCD

Description: The nonperturbative gluon and ghost propagators in Landau gauge QCD are obtained using the Schwinger-Dyson equation approach. The propagator equations are solved in Euclidean space using Landau gauge with a range of vertex inputs. Initially we solve for the ghost alone, using a model gluon input, which leads us to favour a finite ghost dressing in the nonperturbative region. In order to then solve the gluon and ghost equations simultaneously, we find that non-trivial vertices are required, particularly for the gluon propagator in the small momentum limit. We focus on the properties of a number vertices and how these differences influence the final solutions. The self-consistent solutions we obtain are all qualitatively similar and contain a mass-like term in the gluon propagator dressing in agreement with related studies, supporting the long-held proposal of Cornwall.
Date: January 1, 2012
Creator: David J. Wilson, Michael R. Pennington
Partner: UNT Libraries Government Documents Department

Confinement, diquarks and goldstone`s theorem

Description: Determinations of the gluon propagator in the continuum and in lattice simulations are compared. A systematic truncation procedure for the quark Dyson-Schwinger and bound state Bethe-Salpeter equations is described. The procedure ensures the flavor-octet axial- vector Ward identity is satisfied order-by-order, thereby guaranteeing the preservation of Goldstone`s theorem; and identifies a mechanism that simultaneously ensures the absence of diquarks in QCD and their presence in QCD{sup N{sub c}=2}, where the color singlet diquark is the ``baryon`` of the theory.
Date: December 31, 1996
Creator: Roberts, C.D.
Partner: UNT Libraries Government Documents Department

Separable approximation to the Bethe-Salpeter equation in QCD

Description: We calculate the mass spectrum and decay constants of the pseudoscalar meson octet, and mass spectrum of the vector meson octet from a separable approximation to the Bethel-Salpeter equation. In the model, quark propagators inspired by earlier studies of QCD Dyson-Schwinger equations are taken as the only input.
Date: December 1, 1995
Creator: Burden, C.J.; Qian, L. & Roberts, C.D.
Partner: UNT Libraries Government Documents Department

Anomalous {gamma} {r_arrow} 3{pi} amplitude in a bound-state approach

Description: The form factor for the anomalous process {gamma}{pi}{sup +} {r_arrow} pi{sub +}{pi}{sup 0}, which is presently being measured at CEBAF, is calculated in the Schwinger-Dyson approach in conjunction with an impulse approximation. The form factors obtained by the author are compared with the ones predicted by the simple constituent quark loop model, vector meson dominance and chiral perturbation theory, as well as the scarce already available data.
Date: January 1, 2000
Creator: Bistrovic, Bojan & Klabucar, Dubravko
Partner: UNT Libraries Government Documents Department

Continuum regularization of gauge theory with fermions

Description: The continuum regularization program is discussed in the case of d-dimensional gauge theory coupled to fermions in an arbitrary representation. Two physically equivalent formulations are given. First, a Grassmann formulation is presented, which is based on the two-noise Langevin equations of Sakita, Ishikawa and Alfaro and Gavela. Second, a non-Grassmann formulation is obtained by regularized integration of the matter fields within the regularized Grassmann system. Explicit perturbation expansions are studied in both formulations, and considerable simplification is found in the integrated non-Grassmann formalism.
Date: March 1, 1987
Creator: Chan, H.S.
Partner: UNT Libraries Government Documents Department

Dryson equations, Ward identities, and the infrared behavior of Yang-Mills theories. [Schwinger-Dyson equations, Slavnov-Taylor identities]

Description: It was shown using the Schwinger-Dyson equations and the Slavnov-Taylor identities of Yang-Mills theory that no inconsistency arises if the gluon propagator behaves like (1/p/sup 2/)/sup 2/ for small p/sup 2/. To see whether the theory actually contains such singular long range behavior, a nonperturbative closed set of equations was formulated by neglecting the transverse parts of GAMMA and GAMMA/sub 4/ in the Schwinger-Dyson equations. This simplification preserves all the symmetries of the theory and allows the possibility for a singular low-momentum behavior of the gluon propagator. The justification for neglecting GAMMA/sup (T)/ and GAMMA/sub 4//sup (T)/ is not evident but it is expected that the present study of the resulting equations will elucidate this simplification, which leads to a closed set of equations.
Date: January 1, 1979
Creator: Baker, M.
Partner: UNT Libraries Government Documents Department