IR finiteness of the ghost dressing function from numerical resolution of the ghost SD equation

We solve numerically the Schwinger-Dyson (SD hereafter) ghost equation in the Landau gauge for a given gluon propagator finite at k=0 (alpha_gluon=1) and with the usual assumption of constancy of the ghost-gluon vertex ; we show that there exist two possible types of ghost dressing function solutions, as we have previously inferred from analytical considerations : one singular at zero momentum, satisfying the familiar relation alpha_gluon+2 alpha_ghost=0 between the infrared exponents of the gluon and ghost dressing functions(in short, respectively alpha_G and alpha_F) and having therefore alpha_ghost=-1/2, and another which is finite at the origin (alpha_ghost=0), which violates the relation. It is most important that the type of solution which is realized depends on the value of the coupling constant. There are regular ones for any coupling below some value, while there is only one singular solution, obtained only at a critical value of the coupling. For all momenta k<1.5 GeV where they can be trusted, our lattice data exclude neatly the singular one, and agree very well with the regular solution we obtain at a coupling constant compatible with the bare lattice value.Comment: 17 pages, 3 figures (one new figure and a short paragraph added

Divergent IR gluon propagator from Ward-Slavnov-Taylor identities?

We exploit the Ward-Slavnov-Taylor identity relating the 3-gluons to the ghost-gluon vertices to conclude either that the ghost dressing function is finite and non vanishing at zero momentum while the gluon propagator diverges (although it may do so weakly enough not to be in contradiction with current lattice data) or that the 3-gluons vertex is non-regular when one momentum goes to zero. We stress that those results should be kept in mind when one studies the Infrared properties of the ghost and gluon propagators, for example by means of Dyson-Schwinger equations.Comment: 6 pages, bibte

Pseudoscalar qqbar mesons and effective QCD coupling enhanced by <A^2> condensate

Recent developments provided evidence that the dimension 2 gluon condensate is important for the nonperturbative regime of Yang-Mills theories (quantized in the Landau gauge). We show that it may be relevant for the Dyson-Schwinger approach to QCD. In order that this approach leads to a successful hadronic phenomenology, an enhancement of the effective quark-gluon interaction seems to be needed at intermediate (p^2 \sim 0.5 GeV^2) momenta. It is shown that the gluon condensate provides such an enhancement. It is also shown that the resulting effective strong running coupling leads to the sufficiently strong dynamical chiral symmetry breaking and successful phenomenology at least in the light sector of pseudoscalar mesons.Comment: revtex4, 4 eps figures, 8 pages, improved presentation, to appear in Phys. Rev.

The strong coupling constant at small momentum as an instanton detector

We present a study of $\alpha_{MOM}(p)$ at small p computed from the lattice. It shows a dramatic $\propto p^4$ law which can be understood within an instanton liquid model. In this framework the prefactor gives a direct measure of the instanton density in thermalised configurations. A preliminary result for this density is 5.27(4) fm^{-4}.Comment: 12 pages, 4 figure

Non-perturbative Power Corrections to Ghost and Gluon Propagators

We study the dominant non-perturbative power corrections to the ghost and gluon propagators in Landau gauge pure Yang-Mills theory using OPE and lattice simulations. The leading order Wilson coefficients are proven to be the same for both propagators. The ratio of the ghost and gluon propagators is thus free from this dominant power correction. Indeed, a purely perturbative fit of this ratio gives smaller value ($\simeq 270$MeV) of \Lambda_{\ms} than the one obtained from the propagators separately($\simeq 320$MeV). This argues in favour of significant non-perturbative $\sim 1/q^2$ power corrections in the ghost and gluon propagators. We check the self-consistency of the method.Comment: 14 pages, 4 figures; replaced with revised version, to appear in JHE

A Wilson-Yukawa model with a chiral spectrum in 2D

We summarize our recent study of the fermion spectrum in a fermion-scalar 2D model with a chiral $U(1)_L \times U(1)_R$ global symmetry. This model is obtained from a two-cutoff lattice formulation of a 2D U(1) chiral gauge theory, in the limit of zero gauge coupling. The massless fermion spectrum found deep in the vortex phase is undoubled and chiral.Comment: 3 pages, LaTeX, uses espcrc2.sty. To appear in proceedings of Lattice 97, Edinbugh, Scotlan

Wilson Expansion of QCD Propagators at Three Loops: Operators of Dimension Two and Three

In this paper we construct the Wilson short distance operator product expansion for the gluon, quark and ghost propagators in QCD, including operators of dimension two and three, namely, A^2, m^2, m A^2, \ovl{\psi} \psi and m^3. We compute analytically the coefficient functions of these operators at three loops for all three propagators in the general covariant gauge. Our results, taken in the Landau gauge, should help to improve the accuracy of extracting the vacuum expectation values of these operators from lattice simulation of the QCD propagators.Comment: 20 pages, no figure

Testing Landau gauge OPE on the Lattice with a <A2><A^2> Condensate

Using the operator product expansion we show that the $O(1/p^2)$ correction to the perturbative expressions for the gluon propagator and the strong coupling constant resulting from lattice simulations in the Landau gauge are due to a non-vanishing vacuum expectation value of the operator $A^\mu A_\mu$. This is done using the recently published Wilson coefficients of the identity operator computed to third order, and the subdominant Wilson coefficient computed in this paper to the leading logarithm. As a test of the applicability of OPE we compare the $$ estimated from the gluon propagator and the one from the coupling constant in the flavourless case. Both agree within the statistical uncertainty: $\sqrt{} \simeq 1.64(15)$ GeV. Simultaneously we fit \Lams = 233(28) MeV in perfect agreement with previous lattice estimates. When the leading coefficients are only expanded to two loops, the two estimates of the condensate differ drastically. As a consequence we insist that OPE can be applied in predicting physical quantities only if the Wilson coefficients are computed to a high enough perturbative order.Comment: 15 pages, LaTex file with 5 figure