arXiv subjects
Publications and source records attributed to H. Moutarde.
We present a study of $α_{MOM}(p)$ 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}.
We give a more transparent understanding of the vacuum expectation value of the renormalised local operator A^2 by relating it to the gluon propagator integrated over the momentum. The quadratically divergent perturbative contribution is subtracted and the remainder, dominantly due to the O(1/p^2) correction to the perturbative propagator at large p^2 is logarithmically divergent. This provides a transparent derivation of the fact that this O(1/p^2) term is related to the vacuum expectation value of the local A^2 operator and confirms a previous claim based on the operator product expansion (OPE) of the gluon propagator. At leading logarithms the agreement is quantitative, with a standard running factor, between the local A^2 condensate renormalised as described above and the one renormalised in the OPE context.
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.
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.
We argue that the $ $ 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 $ $ is similar to $ $.
The running coupling constant can be estimated by computing gluon two- and three-point Green functions from the lattice. Computing in lattice implies working in a fixed gauge sector (Landau). An source of systematic uncertainty is then the contribution of non gauge-invariant condensates, as $ $, generating power corrections that might still be important at very high energies. We study the impact of this gluon condensate on the analysis of gluon propagator and vertex lattice data and on the estimate of $Λ_{\bar{\rm MS}}$. We finally try a qualitative description of this gluon condensate through the instanton picture
We present preliminary results on the computation of the QCD running coupling constant in the $\widetilde{MOM}$ 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 $1/μ^2$ correction to the asymptotic behaviour, as in the quenched approximation, although a fit without power corrections is still possible with a reasonable $χ^2$. Following the conclusions of our quenched study, we take into account $1/μ^2$ correction to the asymptotic behaviour. We find $Λ_{\rm \bar{MS}}^{N_f=2} = 264(27) {\rm MeV} \times [{a^{-1}(5.6,0.1560)}/{2.19 {\rm GeV}}] $, which leads to $α_s(M_Z) = 0.113(3)(4)$. 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.
We present preliminary results on the computation of the QCD running coupling constant in the MOM_tilde scheme and Landau gauge with two flavours of dynamical Wilson quarks. Gluon momenta range up to about 7 GeV (beta=5.6, 5.8 and 6.0) with a constant dynamical quark mass. This range already allows to exhibit some evidence for a sizeable 1/mu^2 correction to the asymptotic behaviour, as in the quenched approximation. We find Lambda_MS^(N_f=2) = 264(27) MeV x [a^{-1}(5.6,0.1560)/(2.19 GeV)], which leads to alpha_s(M_Z) = 0.113(3)(4). In view of the systematics error to be controlled, this encouraging result is more a preliminary indication than a real prediction.