H. Moutarde

Instantons and the A (2) condensate

We argue that the

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

condensate found in the Landau gauge on lattices, when an Operator Product Expansion of Green functions is performed, might be explained by instantons. We use cooling to estimate the instanton contribution and extrapolate back the result to the thermalised configuration. The resulting

Instantons and condensate

is similar to

Artifacts and ⟨ A 2 ⟩ power corrections: Reexamining Z ψ ( p 2 ) and Z V in the momentum-subtraction scheme

.

Gauge-dependent O.P.E. power corrections on the QCD coupling

We present preliminary results on the computation of the QCD running coupling constant in the scheme and Landau gauge with two flavours of dynamical Wilson quarks. Gluon momenta range up to about 7 GeV (β = 5.6, 5.8 and 6.0) with a constant dynamical-quark mass. This range already allows to exhibit some evidence for a sizable 1/μ2 correction to the asymptotic behaviour, as in the quenched approximation, although a fit without power corrections is still possible with a reasonable χ2. Following the conclusions of our quenched study, we take into account 1/μ2 correction to the asymptotic behaviour. We find = 264(27) MeV × [a−1(5.6,0.1560)/2.19 GeV], which leads to αs(MZ) = 0.113(3)(4). The latter result has to be taken as a preliminary indication rather than a real prediction in view of the systematic errors still to be controlled. Still, being two sigmas below the experimental result makes it very encouraging.

An instanton picture O.P.E. (A2) condensate

Abstract 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 axa0new and very efficient method to eliminate the hypercubic (anisotropy) artifacts based on a systematic expansion on hypercubic invariants which are not SO (4) invariant. Axa0simpler 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.

Artifacts and power corrections: Reexamining Z{sub {psi}}(p{sup 2}) and Z{sub V} in the momentum-subtraction scheme

We give a more transparent understanding of the vacuum expectation value of the renormalized local operator