Multiplicative renormalizability of gluon and ghost propagators in QCD

We reformulate the coupled set of continuum equations for the renormalized gluon and ghost propagators in QCD, such that the multiplicative renormalizability of the solutions is manifest, independently of the specific form of full vertices and renormalization constants. In the Landau gauge, the equations are free of renormalization constants, and the renormalization point dependence enters only through the renormalized coupling and the renormalized propagator functions. The structure of the equations enables us to devise novel truncations with solutions that are multiplicatively renormalizable and agree with the leading order perturbative results. We show that, for infrared power law behaved propagators, the leading infrared behavior of the gluon equation is not solely determined by the ghost loop, as concluded in previous studies, but that the gluon loop, the three-gluon loop, the four-gluon loop, and even massless quarks also contribute to the infrared analysis. In our new Landau gauge truncation, the combination of gluon and ghost loop contributions seems to reject infrared power law solutions, but massless quark loops illustrate how additional contributions to the gluon vacuum polarization could reinstate these solutions. Moreover, a schematic study of the three-gluon and four-gluon loops shows that they too need to be considered in more detail before a definite conclusion about the existence of infrared power behaved gluon and ghost propagators can be reached.Comment: 13 pages, 1 figure, submitted to Phys. Rev.

Effects of quality grade, aging period, blade tenderization, and degree of doneness on tenderness of inside round steaks

We used 162 inside rounds to determine the influence of different quality grades, postmortem aging periods, blade tenderization passes, and degree of doneness on thawing and cooking losses and Warner-Bratzler Shear force (WBS, tenderness). Select (SEL), Choice (CHO), and Certified Angus Beef™ (CAB) inside rounds were aged for 7, 14, or 21 days and not tenderized (0X) or blade tenderized one (1X) or two (2X) times. Steaks from each inside round were assigned randomly to final endpoint cooking temperatures of 150, 160, and 170°F. Percentage of thawing loss was higher (P<.05) for steaks aged 7 days than steaks aged 14 and 21 days. For CHO steaks only, cooking loss was higher (P<.05) for the 2X group compared to the 0X and 1X groups. Steaks aged 14 and 21 days had lower (P<.05) WBS than steaks aged 7 days. Cooking loss and WBS were higher (P<.05) with each increase in endpoint cooking temperature. Postmortem aging (14 or 21 days) and lower endpoint cooking temperatures were the most effective methods to improve WBS of inside round steaks

A hybrid neural network/rule-based technique for on-line gesture and hand-written character recognition

A technique is presented which combines rule-based and neural network pattern recognition methods in an integrated system in order to perform learning and recognition of hand-written characters and gestures in realtime. The GesRec system is introduced which provides a framework for data acquisition, training, recognition, and gesture-to-speech transcription in a Windows environment. A recognition accuracy of 92.5% was obtained for the hybrid system, compared to 89.6% for the neural network only and 82.7% for rules only. Training and recognition times are given for an able-bodied and a disabled user

Multiplicative renormalizability and quark propagator

The renormalized Dyson-Schwinger equation for the quark propagator is studied, in Landau gauge, in a novel truncation which preserves multiplicative renormalizability. The renormalization constants are formally eliminated from the integral equations, and the running coupling explicitly enters the kernels of the new equations. To construct a truncation which preserves multiplicative renormalizability, and reproduces the correct leading order perturbative behavior, non-trivial cancellations involving the full quark-gluon vertex are assumed in the quark self-energy loop. A model for the running coupling is introduced, with infrared fixed point in agreement with previous Dyson-Schwinger studies of the gauge sector, and with correct logarithmic tail. Dynamical chiral symmetry breaking is investigated, and the generated quark mass is of the order of the extension of the infrared plateau of the coupling, and about three times larger than in the Abelian approximation, which violates multiplicative renormalizability. The generated scale is of the right size for hadronic phenomenology, without requiring an infrared enhancement of the running coupling.Comment: 17 pages; minor corrections, comparison to lattice results added; accepted for publication in Phys. Rev.

Constructing the fermion-boson vertex in QED3

We derive perturbative constraints on the transverse part of the fermion-boson vertex in massive QED3 through its one loop evaluation in an arbitrary covariant gauge. Written in a particular form, these constraints naturally lead us to the first non-perturbative construction of the vertex, which is in complete agreement with its one loop expansion in all momentum regimes. Without affecting its one-loop perturbative properties, we also construct an effective vertex in such a way that the unknown functions defining it have no dependence on the angle between the incoming and outgoing fermion momenta. Such a vertex should be useful for the numerical study of dynamical chiral symmetry breaking, leading to more reliable results.Comment: 13 pages, 2 figure

Nonperturbative Renormalization and the QCD Vacuum

We present a self consistent approach to Coulomb gauge Hamiltonian QCD which allows one to relate single gluon spectral properties to the long range behavior of the confining interaction. Nonperturbative renormalization is discussed. The numerical results are in good agreement with phenomenological and lattice forms of the static potential.Comment: 23 pages in RevTex, 4 postscript figure

Strong tree level unitarity violations in the extra dimensional Standard Model with scalars in the bulk

We show how the tree level unitarity violations of compactified extra dimensional extensions of the Standard Model become much stronger when the scalar sector is included in the bulk. This effect occurs when the couplings are not suppressed for larger Kaluza-Klein levels, and could have relevant consequences for the phenomenology of the next generation of colliders. We also introduce a simple and generic formalism to obtain unitarity bounds for finite energies, taking into account coupled channels including the towers of Kaluza-Klein excitations.Comment: Version to appear in Phys. Rev. D Typos corrected and remarks added to clarify figure

The Quark-Photon Vertex and the Pion Charge Radius

The rainbow truncation of the quark Dyson-Schwinger equation is combined with the ladder Bethe-Salpeter equation for the dressed quark-photon vertex to study the low-momentum behavior of the pion electromagnetic form factor. With model gluon parameters previously fixed by the pion mass and decay constant, the pion charge radius $r_\pi$ is found to be in excellent agreement with the data. When the often-used Ball-Chiu Ansatz is used to construct the quark-photon vertex directly from the quark propagator, less than half of $r_\pi^2$ is generated. The remainder of $r^2_\pi$ is seen to be attributable to the presence of the $\rho$-pole in the solution of the ladder Bethe-Salpeter equation.Comment: 21 pages, 9 figure

Regularization-independent study of renormalized non-perturbative quenched QED

A recently proposed regularization-independent method is used for the first time to solve the renormalized fermion Schwinger-Dyson equation numerically in quenched QED$_4$. The Curtis-Pennington vertex is used to illustrate the technique and to facilitate comparison with previous calculations which used the alternative regularization schemes of modified ultraviolet cut-off and dimensional regularization. Our new results are in excellent numerical agreement with these, and so we can now conclude with confidence that there is no residual regularization dependence in these results. Moreover, from a computational point of view the regularization independent method has enormous advantages, since all integrals are absolutely convergent by construction, and so do not mix small and arbitrarily large momentum scales. We analytically predict power law behaviour in the asymptotic region, which is confirmed numerically with high precision. The successful demonstration of this efficient new technique opens the way for studies of unquenched QED to be undertaken in the near future.Comment: 20 pages,5 figure

Non-perturbative Propagators, Running Coupling and Dynamical Quark Mass of Landau gauge QCD

The coupled system of renormalized Dyson-Schwinger equations for the quark, gluon and ghost propagators of Landau gauge QCD is solved within truncation schemes. These employ bare as well as non-perturbative ansaetze for the vertices such that the running coupling as well as the quark mass function are independent of the renormalization point. The one-loop anomalous dimensions of all propagators are reproduced. Dynamical chiral symmetry breaking is found, the dynamically generated quark mass agrees well with phenomenological values and corresponding results from lattice calculations. The effects of unquenching the system are small. In particular the infrared behavior of the ghost and gluon dressing functions found in previous studies is almost unchanged as long as the number of light flavors is smaller than four.Comment: 34 pages, 10 figures, version to be published by Phys. Rev.