Power Corrections to Perturbative QCD and OPE in Gluon Green Functions

We show that QCD Green functions in Landau Gauge exhibit sizable $O(1/\mu^2)$ corrections to the expected perturbative behavior at energies as high as 10 GeV. We argue that these are due to a $$-condensate which does not vanish in Landau gauge.Comment: 3 pages 1 figure lattice2001 (gaugetheories

Gluon propagator, triple gluon vertex and the QCD coupling constant

We study the UV-scaling of the flavorless gluon propagator in the Landau gauge in an energy window up to 9 GeV. Dominant hypercubic lattice artifacts are eliminated. A large set of renormalization schemes is used to test asymptotic scaling. We compare with our results obtained directly from the triple gluon vertex. We end-up with \Lambda_{\bar{\rm{MS}}} = 318(12)(5) MeV and 292(5)(15) MeV respectively for these two methods, compatible which each other but significantly above the Schrodinger method estimate.Comment: 3 pages, LaTeX with two figures; presented at LATTICE9

An Instanton Picture O.P.E. <A^2> Condensate?

Gluon two- and three-point Green Functions computed in Landau gauge from the lattice show the existence of power corrections to the purely perturbative expressions, that can be explained through an Operator Product Expansion as the influence of a non gauge invariant mass dimension two condensate. The relationship of this condensate with topological properties of QCD, namely instantons, will be studied, giving a first estimate of the contribution of instantons to this condensate based in the direct lattice measure, after a cooling process, of the instanton liquid properties.Comment: Lattice2002(topology) contribution, 3 pages, 2 figure

Lattice renormalization of the static quark derivative operator

We give the analytical expressions and numerical values of radiative corrections to the covariant derivative operator on the static quark line, used for the lattice calculation of the Isgur-Wise form factors $\tau_{1/2}(1)$ and $\tau_{3/2}(1)$. Those corrections induce an enhancement of renormalized quantities if an hypercubic blocking is applied to the Wilson line, whereas there is a reduction without such a blocking

O.P.E. and Power Corrections to the QCD coupling constant

Lattice data seems to show that power corrections should be convoked to describe appropriately the transition of the QCD coupling constant running from U.V. to I.R. domains. Those power corrections for the Landau-gauge MOM coupling constant in a pure Yang-Mills theory (N_f=0) are analysed in terms of Operator Product Expansion (O.P.E.) of two- and three-point Green functions, the gluon condensate emerging from this study. The semi-classical picture given by instantons can be also used to look for into the nature of the power corrections and gluon condensate.Comment: 5 pages, talk given at XXX International Meeting on Fundamental Physics, Jaca 200

Temperature and pressure dependence of the infrared spectrum of 1-ethyl-3-methylimidazolium trifluoromethanesulfonate ionic liquid

The infrared absorption spectrumof 1-ethyl-3-methylimidazoliumtrifluoromethanesulfonate (EMI-TfO) was investigated at ambient pressure and variable temperatures between 120 and 330 K, or at roomtemperature and variable pressures up to 10 GPa. Upon cooling, the ionic liquid crystallizes; on the contrary, upon compression no evidence of crystallization can be obtained from the infrared spectra. Moreover, Density Functional Theory (DFT) calculations were applied to gain a better description of the ionic couple. The !B97X-D functional, including not only the empirical dispersion corrections but also the presence of a polar solvent, gives a good agreement with the infrared spectrum and suggests that TfO resides above the plane of the imidazolium, with the shorter distance between the O atom of the anion and the C2 atom of the imidazolium ring equal to 2.23 A

Quark propagator and vertex: systematic corrections of hypercubic artifacts from lattice simulations

This is the first part of a study of the quark propagator and the vertex function of the vector current on the lattice in the Landau gauge and using both Wilson-clover and overlap actions. In order to be able to identify lattice artifacts and to reach large momenta we use a range of lattice spacings. The lattice artifacts turn out to be exceedingly large in this study. We present a new and very efficient method to eliminate the hypercubic (anisotropy) artifacts based on a systematic expansion on hypercubic invariants which are not SO(4) invariant. A simpler version of this method has been used in previous works. This method is shown to be significantly more efficient than the popular ``democratic'' methods. It can of course be applied to the lattice simulations of many other physical quantities. The analysis indicates a hierarchy in the size of hypercubic artifacts: overlap larger than clover and propagator larger than vertex function. This pleads for the combined study of propagators and vertex functions via Ward identities.Comment: 14 pags., 9 fig

Consistent OPE Description of Gluon Two- and Three-point Green Function?

We perform an OPE analysis of the flavorless non-perturbative gluon propagator and the symmetric three-gluon vertex in the Landau gauge. The first subdominant operator is $A_\mu A^\mu$ which can condensate in the Landau gauge ``vacuum'' although being a non-gauge invariant operator. We neglect all higher dimension operators. Then the gluon propagator and the symmetric three gluon vertex only depend on one common unknown condensate. We propose a consistency check from lattice data. At two loops for the leading coefficient and with $1/p^2$ corrections at tree-level order the two fitted values for the condensate do not agree. At three loops we argue that the today unknown $\beta_2^{\rm MOM}$ should be equal to $1.5(3)\times \beta_2^{\widetilde{\rm MOM}}=7400(1500)$ to fulfill the OPE relation. Inclusion of the power corrections' anomalous dimensions should improve further the agreement. We show that these techniques cannot be applied to the asymmetric three gluon vertex with one vanishing momentum.Comment: latex-file,10 figs.,13 pg

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