The running coupling of 8 flavors and 3 colors

Zoltan Fodor,Julius Kuti,Daniel Nogradi,Chik Him Wong,Kieran Holland,Santanu Mondal

doi:10.1007/jhep06(2015)019

Abstract

We compute the renormalized running coupling of SU(3) gauge theory coupled to N f = 8 flavors of massless fundamental Dirac fermions. The recently proposed finite volume gradient flow scheme is used. The calculations are performed at several lattice spacings allowing for a controlled continuum extrapolation. The results for the discrete β-function show that it is monotonic without any sign of a fixed point in the range of couplings we cover. As a cross check the continuum results are compared with the well-known perturbative continuum β-function for small values of the renormalized coupling and perfect agreement is found.

Highlights

The calculations are performed at several lattice spacings allowing for a controlled continuum extrapolation
The running coupling using the Schroedinger functional was investigated in [3], the thermodynamics of the model was studied in [4] and hadron spectroscopy was presented in [5, 6]. These studies agreed in their conclusion that the model is outside the conformal window and spontaneous chiral symmetry breaking takes place
In [7] the mass anomalous dimension was investigated but a definite conclusion whether the model is inside or outside the conformal window could not be drawn from the data

Summary

The gradient flow running coupling scheme

In order to investigate the infrared behavior of a model the running coupling is a natural choice. In the current work the recently proposed finite volume gradient flow scheme [9, 10] is used, which is based on Luscher’s Wilson flow [11,12,13,14] related to earlier constructions by Morningstar and Peardon [15] as well as Lohmayer and Neuberger [16] In this scheme a 1-parameter family of couplings is defined in finite 4-volume by gc. Tree-level improvement is not sensitive to fermionic radiative corrections The application of the gradient flow is not by any means limited to running coupling studies, applications include scale setting in QCD [33,34,35,36], thermodynamics [37], renormalized energy momentum tensor [38,39,40], various aspects of chiral symmetry [41,42,43] and scalar glueballs [44]

Numerical simulation

Continuum extrapolation

Systematic error

Final results

Findings

Conclusion and outlook