# Instanton dominance over $$a_s$$ 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 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.

- Authors:

- Cyprus Institute, Nicosia, Cyprus
- Univ. Paris-Sud, Orsay (France)
- Univ. Pablo de Olavide, 41013 Sevilla; Spain; Univ. of Granada (Spain)
- Universidad de Huelva, 21071 Huelva; Spain; Univ. of Granada (Spain)
- College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Heidelberg Univ. (Germany). Inst. for Theoretische Physik

- Publication Date:

- Research Org.:
- Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- OSTI Identifier:
- 1434241

- Report Number(s):
- JLAB-THY-18-2689; DOE/OR/23177-4421; arXiv:1802.01342

- DOE Contract Number:
- AC05-06OR23177

- Resource Type:
- Conference

- Resource Relation:
- Journal Name: EPJ Web of Conferences; Journal Volume: 175; Conference: Lattice 2017, 35th International Symposium on Lattice Field Theory, 18-24 Jun 2017. Granada, Spain

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Athenodorou, Andreas, Boucaud, Philippe, de Soto, Feliciano, Rodriguez-Quintero, Jose, and Zafeiropoulos, Savvas.
```*Instanton dominance over $a_s$ at low momenta from lattice QCD simulations at $N_f=0$, $N_f=2+1$ and $N_f=2+1+1$*. United States: N. p., 2018.
Web. doi:10.1051/epjconf/201817512011.

```
Athenodorou, Andreas, Boucaud, Philippe, de Soto, Feliciano, Rodriguez-Quintero, Jose, & Zafeiropoulos, Savvas.
```*Instanton dominance over $a_s$ at low momenta from lattice QCD simulations at $N_f=0$, $N_f=2+1$ and $N_f=2+1+1$*. United States. doi:10.1051/epjconf/201817512011.

```
Athenodorou, Andreas, Boucaud, Philippe, de Soto, Feliciano, Rodriguez-Quintero, Jose, and Zafeiropoulos, Savvas. Sun .
"Instanton dominance over $a_s$ at low momenta from lattice QCD simulations at $N_f=0$, $N_f=2+1$ and $N_f=2+1+1$". United States.
doi:10.1051/epjconf/201817512011. https://www.osti.gov/servlets/purl/1434241.
```

```
@article{osti_1434241,
```

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

author = {Athenodorou, Andreas and Boucaud, Philippe and de Soto, Feliciano and Rodriguez-Quintero, Jose and Zafeiropoulos, Savvas},

abstractNote = {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.},

doi = {10.1051/epjconf/201817512011},

journal = {EPJ Web of Conferences},

number = ,

volume = 175,

place = {United States},

year = {Sun Apr 01 00:00:00 EDT 2018},

month = {Sun Apr 01 00:00:00 EDT 2018}

}