Two-loop Improved Truncation of the Ghost-Gluon Dyson-Schwinger Equations: Multiplicatively Renormalizable Propagators and Nonperturbative Running Coupling

The coupled Dyson-Schwinger equations for the gluon and ghost propagators are investigated in the Landau gauge using a two-loop improved truncation that preserves the multiplicative renormalizability of the propagators. In this truncation all diagrams contribute to the leading order infrared analysis. The infrared contributions of the nonperturbative two-loop diagrams to the gluon vacuum polarization are computed analytically, and this reveals that infrared power behaved propagator solutions only exist when the squint diagram contribution is taken into account. For small momenta the gluon and ghost dressing functions behave respectively like (p^2)^{2\kappa} and (p^2)^{-\kappa}, and the running coupling exhibits a fixed point. The values of the infrared exponent and fixed point depend on the precise details of the truncation. The coupled ghost-gluon system is solved numerically for all momenta, and the solutions have infrared behaviors consistent with the predictions of the infrared analysis. For truncation parameters chosen such that \kappa=0.5, the two-loop improved truncation is able to produce solutions for the propagators and running coupling which are in very good agreement with recent lattice simulations.Comment: 41 pages, LateX; minor corrections; accepted for publication in Few-Body System

Comment on "Nucleon form factors and a nonpointlike diquark"

Authors of Phys. Rev. C 60, 062201 (1999) presented a calculation of the electromagnetic form factors of the nucleon using a diquark ansatz in the relativistic three-quark Faddeev equations. In this Comment it is pointed out that the calculations of these form factors stem from a three-quark bound state current that contains overcounted contributions. The corrected expression for the three-quark bound state current is derived.Comment: 6 pages, 1 figure, revtex, eps

K -> pi pi and a light scalar meson

We explore the Delta-I= 1/2 rule and epsilon'/epsilon in K -> pi pi transitions using a Dyson-Schwinger equation model. Exploiting the feature that QCD penguin operators direct K^0_S transitions through 0^{++} intermediate states, we find an explanation of the enhancement of I=0 K -> pi pi transitions in the contribution of a light sigma-meson. This mechanism also affects epsilon'/epsilon.Comment: 7 pages, REVTE

Numerical cancellation of photon quadratic divergence in the study of the Schwinger-Dyson equations in Strong Coupling QED

The behaviour of the photon renormalization function in strong coupling QED has been recently studied by Kondo, Mino and Nakatani. We find that the sharp decrease in its behaviour at intermediate photon momenta is an artefact of the method used to remove the quadratic divergence in the vacuum polarization. We discuss how this can be avoided in numerical studies of the Schwinger-Dyson equations.Comment: 9 pages, Latex, 5 figures. Complete postscript file available from: ftp://cpt1.dur.ac.uk/pub/preprints/dtp94/dtp94100/dtp94100.p

QCD in the Infrared with Exact Angular Integrations

In a previous paper we have shown that in quantum chromodynamics the gluon propagator vanishes in the infrared limit, while the ghost propagator is more singular than a simple pole. These results were obtained after angular averaging, but in the current paper we go beyond this approximation and perform an exact calculation of the angular integrals. The powers of the infrared behaviour of the propagators are changed substantially. We find the very intriguing result that the gluon propagator vanishes in the infrared exactly like p^2, whilst the ghost propagator is exactly as singular as 1/p^4. We also find that the value of the infrared fixed point of the QCD coupling is much decreased from the y-max estimate: it is now equal to 4\pi/3.Comment: 7 pages, late

Running Coupling in Non-Perturbative QCD - I. Bare Vertices and y-max Approximation

A recent claim that in quantum chromodynamics the gluon propagator vanishes in the infrared limit, while the ghost propagator is more singular than a simple pole, is investigated analytically and numerically. This picture is shown to be supported even at the level in which the vertices in the Dyson-Schwinger equations are taken to be bare. The running coupling is shown to be uniquely determined by the equations and to have a large finite infrared limit.Comment: Latex, 41 pages, 7 figures, submitted to Phys. Rev. D; corrected typo

Resonant control of spin dynamics in ultracold quantum gases by microwave dressing

We study experimentally interaction-driven spin oscillations in optical lattices in the presence of an off-resonant microwave field. We show that the energy shift induced by this microwave field can be used to control the spin oscillations by tuning the system either into resonance to achieve near-unity contrast or far away from resonance to suppress the oscillations. Finally, we propose a scheme based on this technique to create a flat sample with either singly- or doubly-occupied sites, starting from an inhomogeneous Mott insulator, where singly- and doubly-occupied sites coexist.Comment: 4 pages, 5 figure