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

¹ Computation-based Science and Technology Research Center, Cyprus Institute, 20 Kavafi Str., Nicosia 2121, Cyprus
² Laboratoire de Physique Théorique (UMR8627), CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
³ Dpto. Sistemas Físicos, Químicos y Naturales, Univ. Pablo de Olavide, 41013 Sevilla ; Spain
⁴ Dpto. Ciencias Integradas, Fac. Ciencias Experimentales; Universidad de Huelva, 21071 Huelva ; Spain.
⁵ Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA
⁶ Department of Physics, College of William and Mary, Williamsburg, VA 23187-8795, USA
⁷ Institute for Theoretical Physics, Universität Heidelberg, Philosophenweg 12, D-69120 Germany
⁸ CAFPE, Universidad de Granada, E-18071 Granada, Spain

^* Speaker, e-mail: fcsotbor@upo.es

Published online: 26 March 2018

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, 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, Λ_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.