Abstract
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.
Highlights
Instantons and other semi-classical solutions of the QCD Lagrangian are believed to play an essential role in the low energy dynamics of QCD, where the crucial phenomena of confinement and chiral symmetry breaking take place [1]
This finding serves as a confirmation that the low momenta correlations are dominated by instanton-like objects, and allows to extract the instanton density without need for any filtering technique
The IR running of αMOM(k) for N f = 0, N f = 2 + 1, and N f = 2 + 1 + 1 has been analyzed, and fits nicely to an uncorrelated instanton liquid model for momenta k ∈ (0.3, 0.9) GeV
Summary
Instantons and other semi-classical solutions of the QCD Lagrangian are believed to play an essential role in the low energy dynamics of QCD, where the crucial phenomena of confinement and chiral symmetry breaking take place [1]. Instantons are intimately related to the topological properties of the QCD gauge fields, inherently non-perturbative and one can study their effects via lattice simulations. They are very important since among others they can provide a resolution to the U(1) problem, provide a mechanism of chiral symmetry breaking, they can be responsible for rare decays of baryons. Different smearing methods and, more recently, Wilson flow are efficient techniques that remove short-range fluctuations in the gauge fields that have been widely exploited for the study of QCD topology [2, 3].
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