QCD tests with an infrared finite gluon propagator and coupling constant

Recent progress in the solution of Schwinger-Dyson equations, as well as lattice simulation of pure glue QCD, indicate that the gluon propagator and coupling constant are infrared finite. Such non-perturbative information can be introduced in the QCD perturbative expansion in the scheme named Dynamical Perturbation Theory. We exemplify this procedure with the calculation of some two-body non-leptonic annihilation B meson decays, which show agreement with the experimental data in the case of a gluon propagator characterized by a dynamical gluon mass of 500MeV, compatible with the value found in several processes computed with this method. We give a. preliminary account of the application of this procedure at the loop level in the case of the Bjorken sum rule.

Thermodynamics of quasi-particles at finite chemical potential

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Infrared finite solutions for the gluon propagator and the QCD vacuum energy

Nonperturbative infrared finite solutions for the gluon polarization tensor have been found, and the possibility that gluons may have a dynamically generated mass is supported by recent Monte Carlo simulation on the lattice. These solutions differ among themselves, due to different approximations performed when solving the Schwinger-Dyson equations for the gluon polarization tensor. Only approximations that minimize energy are meaningful, and, according to this, we compute an effective potential for composite operators as a function of these solutions in order to distinguish which one is selected by the vacuum. © 1997 Elsevier Science B.V.

QCD phenomenology with infrared finite SDE solutions

Recent progress in the solution of Schwinger-Dyson equations (SDE), as well as lattice simulation of pure glue QCD, indicate that the gluon propagator and coupling constant are infrared (IR) finite. We discuss how this non-perturbative information can be introduced into the QCD perturbative expansion in a consistent scheme, showing some examples of tree level hadronic reactions that successfully fit the experimental data with the gluon propagator and coupling constant depending on a dynamically generated gluon mass. This infrared mass scale acts as a natural cutoff and eliminates some of the ad hoc parameters usually found in perturbative QCD calculations. The application of these IR finite Green's functions in the case of higher order terms of the perturbative expansion is commented. © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.

NUMERICAL SIMULATION of CONVECTION-DIFFUSION PROBLEMS BY THE CONTROL-VOLUME-BASED FINITE-ELEMENT METHOD

This work presents a numerical study of the tri-dimensional convection-diffusion equation by the control-volume-based on finite-element method using quadratic hexahedral elements. Considering that the equation governing this problem in its main variable may represent several properties, including temperature, turbulent kinetic energy, viscous dissipation rate of the turbulent kinetic energy, specific dissipation rate of the turbulent kinetic energy, or even the concentration of a contaminant in a given medium, among others, the wide applicability of this problem is thus evidenced. Three cases of temperature distributions will be studied specifically in this work, in addition to one case of pollutant dispersion upon analysis of the concentration of a contaminant in a fixed flow point. Some comparisons will be carried out against works found in the open literature, while others will be done according to each phenomenon characteristics.

Freezing of the QCD coupling constant and the pion form factor

The possibility that the QCD coupling constant (alpha(s)) has an infrared finite behavior (freezing) has been extensively studied in recent years. We compare phenomenological values of the frozen QCD running coupling between different classes of solutions obtained through non-perturbative Schwinger-Dyson Equations. With these solutions were computed QCD predictions for the asymptotic pion form factor which, in turn, were compared with experiment.

Coulomb gauge quark model, vacuum condensates and high density quark matter

We consider here a Coulomb gauge quark model which includes an explicit construct for a nontrivial vacuum structure in QCD at finite density. Non-perturbative renormalization of ultraviolet diverges is performed by adding counterterms. The equation of state for u and d quark matter at zero temperature is calculated in the Hartree-Fock approximation.

Freezing of the QCD coupling constant and solutions of Schwinger-Dyson equations

We compare phenomenological values of the frozen QCD running coupling constant (alpha(s)) with two classes of infrared finite solutions obtained through nonperturbative Schwinger-Dyson equations. We use these same solutions with frozen coupling constants as well as their respective nonperturbative gluon propagators to compute the QCD prediction for the asymptotic pion form factor. Agreement between theory and experiment on alpha(s)(0) and F (pi)(Q(2)) is found only for one of the Schwinger-Dyson equation solutions.

QCD effective charge and the structure function F-2 at small-x

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Study of the (D)over-barN Interaction in a QCD Coulomb Gauge Quark Model

We study the (D) over barN interaction at low energies with a quark model inspired in the QCD Hamiltonian in Coulomb gauge. The model Hamiltonian incorporates a confining Coulomb potential extracted from a self-consistent quasiparticle method for the gluon degrees of freedom, and transverse-gluon hyperfine interaction consistent with a finite gluon propagator in the infrared. Initially a constituent-quark mass function is obtained by solving a gap equation and baryon and meson bound-states are obtained in Fock space using a variational calculation. Next, having obtained the constituent-quark masses and the hadron waves functions, an effective meson-nucleon interaction is derived from a quark-interchange mechanism. This leads to a short range meson-baryon interaction and to describe long-distance physics vector- and scalar-meson exchanges described by effective Lagrangians are incorporated. The derived effective (D) over barN potential is used in a Lippmann-Schwinger equation to obtain phase shifts. The results are compared with a recent similar calculation using the nonrelativistic quark model.

The spectrum of D-slash in QCD via replicas

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

ZERO SOUND-VELOCITY IN PI, RHO-MESON GASES

Sharp transitions are perhaps absent in QCD, so that one looks for physical quantities which may reflect the phase change. One such quantity is the sound velocity which was shown in lattice theory to become zero at the transition point for pure glue. We show that even in a simple bag model the sound velocity goes to zero at temperature T = T(v) not-equal 0 and that the numerical value of this T(v) depends on the nature of the meson. The average thermal energy of mesons goes linearly with T near T(v), with much smaller slope for the pion. The T(v) - s can be connected with the Boltzmann temperatures obtained from transverse momentum spectrum of these mesons in heavy-ion collision at mid-rapidity. It would be interesting to check the presence of different T(v) - s in present day finite T lattice theory.

A finite element free convection model for the side wall heated cavity

This paper presents a finite element numerical solution of free convection in a cavity with side walls maintained at constant but different temperatures. The predictions from the model and the method of solution were validated by comparison with the 'bench mark' solution and Vahl Davis' results and good agreement was found. The present model was used to obtain additional results over a wide range of Rayleigh number (10(3)-10(6)) and L/H ratios varying from 0.1 to 1.0. The predicted stream function patterns, temperature and velocity profiles as well as the mean Nusselt number were presented and discussed. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

QCD phase transitions from relativistic hadron models

The models of translationally invariant infinite nuclear matter in the relativistic mean field models are very interesting and simple, since the nucleon can connect only to a constant vector and scalar meson field. Can one connect these to the complicated phase transitions of QCD? For an affirmative answer to this question, one must consider models where the coupling contstants to the scalar and vector fields depend on density in a nonlinear way, since as such the models are not explicitly chirally invariant. Once this is ensured, indeed one can derive a quark condensate indirectly from the energy density of nuclear matter which goes to zero at large density and temperature. The change to zero condensate indicates a smooth phase transition. © Springer-Verlag 1996.

Infrared finite gluon propagator and the structure of chiral symmetry breaking

We study the chiral symmetry breaking in QCD, using an effective potential for composite operators, with infrared finite gluon propagators that have been found by numerical calculation of the Schwinger-Dyson equations as well as in lattice simulations. The existence of a gluon propagator that is finite at k2 = 0 modifies substantially the transition between the phases with and without chiral symmetry.