L. von Smekal

Nucleon properties in the covariant quark-diquark model

In the covariant quark-diquark model the effective Bethe-Salpeter (BS) equations for the nucleon and the Δ are solved including scalar and axial vector diquark correlations. Their quark substructure is effectively taken into account in both, the interaction kernel of the BS equations and the currents employed to calculate nucleon observables. Electromagnetic current conservation is maintained. The electric form factors of proton and neutron match the data. Their magnetic moments improve considerably by including axial vector diquarks and photon induced scalar-axial vector transitions. The isoscalar magnetic moment can be reproduced, the isovector contribution is about 15% too small. The ratio µGE/GM and the axial and strong couplings gA, gπNN, provide an upper bound on the relative importance of axial vector diquarks confirming that scalar diquarks nevertheless describe the dominant 2-quark correlations inside nucleons.

Comparing SU(2) to SU(3) gluodynamics on large lattices

Also cited as: Lattice 2007, the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, Germany / Gunnar Bali, Vladimir Braun, Christof Gattringer, Meinulf Gockeler, Andreas Schafer, Peter Weisz, Tilo Wettig (eds.): pp. 340/1-340/7.

Infrared behavior of gluons and ghosts in ghost-antighost symmetric gauges

To investigate the possibility of a ghost-antighost condensate the coupled Dyson--Schwinger equations for the gluon and ghost propagators in Yang--Mills theories are derived in general covariant gauges, including ghost-antighost symmetric gauges. The infrared behaviour of these two-point functions is studied in a bare-vertex truncation scheme which has proven to be successful in Landau gauge. In all linear covariant gauges the same infrared behaviour as in Landau gauge is found: The gluon propagator is infrared suppressed whereas the ghost propagator is infrared enhanced. This infrared singular behaviour provides indication against a ghost-antighost condensate. In the ghost-antighost symmetric gauges we find that the infrared behaviour of the gluon and ghost propagators cannot be determined when replacing all dressed vertices by bare ones. The question of a BRST invariant dimension two condensate remains to be further studied.

Current conservation in the covariant quark-diquark model of the nucleon

The description of baryons as fully relativistic bound states of quark and glue reduces to an effective Bethe-Salpeter equation with quark-exchange interaction when irreducible 3-quark interactions are neglected and separable 2-quark (diquark) correlations are assumed. This covariant quark-diquark model of baryons is studied with the inclusion of the quark substructure of the diquark correlations. In order to maintain electromagnetic current conservation it is then necessary to go beyond the impulse approximation. A conserved current is obtained by including the coupling of the photon to the exchanged quark and direct “seagull” couplings to the diquark structure. Adopting a simple dynamical model of constituent quarks and exploring various parametrisations of scalar diquark correlations, the nucleon Bethe-Salpeter equation is solved and the proton and neutron electromagnetic form factors are calculated numerically. The resulting magnetic moments are still about 50% too small, the improvements necessary to remedy this are discussed. The results obtained in this framework provide an excellent description of the electric form factors (and charge radii) of the proton, up to a photon momentum transfer of 3.5 GeV2, and the neutron.

Solving a Coupled Set of Truncated QCD Dyson-Schwinger Equations

Abstract Truncated Dyson—Schwinger equations represent finite subsets of the equations of motion for Greens functions. Solutions to these nonlinear integral equations can account for nonperturbative correlations. A closed set of coupled Dyson—Schwinger equations for the propagators of gluons and ghosts in Landau gauge QCD is obtained by neglecting all contributions from irreducible 4-point correlations and by implementing the Slavnov—Taylor identities for the 3-point vertex functions. We solve this coupled set in an one-dimensional approximation which allows for an analytic infrared expansion necessary to obtain numerically stable results. This technique, which was also used in our previous solution of the gluon Dyson—Schwinger equation in the Mandelstam approximation, is here extended to solve the coupled set of integral equations for the propagators of gluons and ghosts simultaneously. In particular, the gluon propagator is shown to vanish for small spacelike momenta whereas the previously neglected ghost propagator is found to be enhanced in the infrared. The running coupling of the nonperturbative subtraction scheme approaches an infrared stable fixed point at a critical value of the coupling, α c ⋍ 9.5.

QCD Lambda parameter from Landau-gauge gluon and ghost correlations

We utilise a recently developed minimal MOM scheme to determine the QCD Lambda parameter from the gluon and ghost propagators in lattice Landau gauge. We discuss uncertainties in the analysis and report our preliminary zero and two flavour results, which are r_0*LambdaMS^{(0)}=0.62(1) and r_0*LambdaMS^{(2)}=0.60(3)(2), with the second error due to an extrapolation uncertainty.

Role of center vortices in chiral symmetry breaking in SU(3) gauge theory

Patrick O. Bowman, Kurt Langfeld, Derek B. Leinweber, Andre Sternbeck, Lorenz von Smekal, and Anthony G. Williams

Solving the Gluon Dyson-Schwinger Equation in the Mandelstam Approximation

Abstract Truncated Dyson—Schwinger equations represent finite subsets of the equations of motion for Greens functions. Solutions to these nonlinear integral equations can account for nonperturbative correlations. We describe the solution to the Dyson—Schwinger equation for the gluon propagator of Landau gauge QCD in the Mandelstam approximation. This involves a combination of numerical and analytic methods: an asymptotic infrared expansion of the solution is calculated recursively. In the ultraviolet, the problem reduces to an analytically solvable differential equation. The iterative solution is then obtained numerically by matching it to the analytic results at appropriate points. Matching point independence is obtained for sufficiently wide ranges. The solution is used to extract a nonperturbative β -function. The scaling behavior is in good agreement with perturbative QCD. No further fixed point for positive values of the coupling is found which thus increases without bound in the infrared. The nonperturbative result implies an infrared singular quark interaction relating the scale A of the subtraction scheme to the string tension σ .

Curci-Ferrari mass and the Neuberger problem

We study the massive Curci-Ferrari model as a starting point for defining BRST quantisation for Yang-Mills theory on the lattice. In particular, we elucidate this proposal in light of topological approaches to gauge-fixing and study the case of a simple one-link Abelian model.

Relativistic Three-Quark Bound States in Separable Two-Quark Approximation

Baryons as relativistic bound states in 3-quark correlations are described by an effective Bethe-Salpeter equation when irreducible 3-quark interactions are neglected and separable 2-quark correlations are assumed. We present an efficient numerical method to calculate the nucleon mass and its covariant wave function in this quantum field theoretic quark-diquark model with quark-exchange interaction. Expanding the components of the spinorial wave function in terms of Chebyshev polynomials, the four-dimensional integral equations are in a first step reduced to a coupled set of one-dimensional ones. This set of linear and homogeneous equations defines a generalised eigenvalue problem. Representing the eigenvector corresponding to the largest eigenvalue, the Chebyshev moments are then obtained by iteration. The nucleon mass is implicitly determined by the eigenvalue, and its covariant wave function is reconstructed from the moments within the Chebyshev approximation.