Heavy quarkonium potential at nonzero temperature in the instanton liquid model

Within the framework of the instanton Liquid Model (ILM) we evaluate the heavy quark [Formula: see text] potential at finite temperature. The potential in the ILM has two components: direct instantons contribution and the ILM modified one-gluon exchange contribution. The dynamical ”electric” mass [Formula: see text], which was generated by rescattering of the gluons from the ILM instantons, was taken into account.

Instanton dominance over αs at low momenta from lattice QCD simulations at Nf = 0, Nf = 2 + 1 and Nf = 2 + 1 + 1

We report on an instanton-based analysis of the gluon Green functions in the Landau gauge for low momenta; in particular we use lattice results for αs in the symmetric momentum subtraction scheme (MOM) for large-volume lattice simulations. We have exploited quenched gauge field configurations, Nf = 0, with both Wilson and tree-level Symanzik improved actions, and unquenched ones with Nf = 2 + 1 and Nf = 2 + 1 + 1 dynamical flavors (domain wall and twisted-mass fermions, respectively). We show that the dominance of instanton correlations on the low-momenta gluon Green functions can be applied to the determination of phenomenological parameters of the instanton liquid and, eventually, to a determination of the lattice spacing. We furthermore apply the Gradient Flow to remove short-distance fluctuations. The Gradient Flow gets rid of the QCD scale, ΛQCD, and reveals that the instanton prediction extents to large momenta. For those gauge field configurations free of quantum fluctuations, the direct study of topological charge density shows the appearance of large-scale lumps that can be identified as instantons, giving access to a direct study of the instanton density and size distribution that is compatible with those extracted from the analysis of the Green functions.

Gluons, Heavy and Light Quarks in the QCD Vacuum

We are discussing the properties of the QCD vacuum which might be important especially for the understanding of hadrons with small quark core size ~ 0:3 fm: We assume that at these distances the QCD vacuum can be described by the Instanton Liquid Model (ILM). At larger distances, where confinement is important, ILM should be extended to Dyons Liquid Model (DLM). The ILM has only two free parameters, average instanton size ρ ≈ 0:3 fm and average inter-instanton distance R ≈ 1 fm, and can successfully describe the key features of light hadron physics. One of the important conceptual results was prediction of the momentum dependent dynamical quark mass M ~ (packing f raction)1/2 ρ-1 ≈ 360 MeV, later confirmed numerically by evaluations in the lattice. The estimates show that gluon-instanton interaction strength is also big and is controlled by the value of dynamical gluon mass Mg ≈ M. Heavy quarks interact with instantons much weaker. The heavy quark-instanton interaction strength is given by ΔmQ ~ packing fraction ρ-1 ≈ 70 MeV: Nevertheless, the direct instanton contribution to the colorless heavy-heavy quarks potential is sizable and must be taken into account. At small distances, where one-gluon exchange contribution to this potential is dominated, we have to take into account dynamical gluon mass Mg. Also, instantons are generating light-heavy quarks interactions and allow to describe the nonperturbative effects in heavy-light quarks systems.