New scheme for the running coupling constant in gauge theories using Wilson loops

Abstract

We propose a new renormalization scheme of the running coupling constant in general gauge theories using the Wilson loops. The renormalized coupling constant is obtained from the Creutz ratio in lattice simulations and the corresponding perturbative coefficient at the leading order. The latter can be calculated by adopting the zeta-function resummation techniques. We perform a benchmark test of our scheme in quenched QCD with the plaquette gauge action. The running of the coupling constant is determined by applying the step-scaling procedure. Using several methods to improve the statistical accuracy, we show that the running coupling constant can be determined in a wide range of energy scales with relatively small number of gauge configurations. * ) Here we take the continuum limit and estimate the systematic error in the same way as we did in subsection 4.3.

Non-perturbative determination of the Λ-parameter in the pure SU(3) gauge theory from the twisted gradient flow coupling

“…Several other schemes are also available to define the running coupling with the step scaling method [13][14][15][16][17]. The gradient flow scheme is one of the applications of the gradient flow method, in which the gauge field is smeared with the so-called flow equation and the smeared gauge field has a nice perturbative property on the renormalizability [18][19][20].…”

“…• Set (A): all data pairs at L/a = (12, 18), (16,24), or (24,36) in each β row listed in table 1. This corresponds to u max 6.848.…”

Study of the scaling properties in SU(2) gauge theory with eight flavors

“…We also introduce the method for the coupling constant by using Wilson loop [16]. We first use the Creutz ratio in a finite volume (L/a) 4 as Taking different directions such as twisted-twisted direction corresponds to the different scheme of defining of the renormalized couplings.…”

“…Since χ(r, L/a) itself has a systematic artifact from discretization [16,11], it is better to improve g 2 W (r) by using discretized value of the leading factor k(r) instead of its continuum value which is calculated in a lattice perturbation [11]. While both the k(r) and χ(r) contain large lattice artifacts, some of them may be canceled each other and the ratio χ(r)/k(r) could behave as a smooth continuous function of r.…”

Search for the IR fixed point in the Twisted Polyakov Loop scheme (II)

“…Appelquist et al performed lattice calculation of the running coupling constant in the Schrödinger functional (SF) scheme and discovered evidence of an IR fixed point in the case of N f = 12 [6]. On the other hand, Fodor et al does not obtain a signal of IR fixed point using the different scheme based on the Wilson loop [7,8]. The difficulty is mainly due to scheme dependence of the running coupling constant and the presence of significant lattice artifacts in the strong-coupling regime.…”