Instanton dominance over ${\alpha }_s$ at low momenta from lattice QCD simulations at $N_f=0$, $N_f=2+1$ and $N_f=2+1+1$

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 ${\alpha }_s$ in the symmetric momentum subtraction scheme ($\mathrm{MOM}$) for large-volume lattice simulations. We have exploited quenched gauge field configurations, $N_f=0$, with both Wilson and tree-level Symanzik improved actions, and unquenched ones with $N_f=2+1$ and $N_f=2+1+1$ 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, ${\Lambda }_{\mathrm{QCD}}$, 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.

arXiv commentProceedings of the 35th International Symposium on Lattice Field Theory, Granada, Spain

References in corpus (20)

• Instantons in QCD
• Properties and uses of the Wilson flow in lattice QCD
• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Domain wall QCD with physical quark masses
• Light hadrons from lattice QCD with light (u,d), strange and charm dynamical quarks
• On the zero crossing of the three-gluon vertex
• Instantons from over-improved cooling
• Topological Structure of the SU(3) Vacuum
• Comparison of the gradient flow with cooling in $SU(3)$ pure gauge theory
• Instantons, the QCD Vacuum, and Hadronic Physics
• Refining the detection of the zero crossing for the symmetric and asymmetric three-gluon vertices
• The strong coupling constant at small momentum as an instanton detector
• Topological charge using cooling and the gradient flow
• Cooling and the SU(2) Instanton Vaccuum
• Modified instanton profile effects from lattice Green functions
• Impact of Dynamical Fermions on QCD Vacuum Structure
• Gluon Green functions free of Quantum fluctuations
• The topological susceptibility and f_pi from lattice QCD
• Quark Propagation in the Instantons of Lattice QCD
• Are the low-momentum gluon correlations semiclassically determined?

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