The static potential with hypercubic blocking

Abstract

We measure the static potential from Wilson loops constructed using hypercubic blocked (HYP) links. The HYP potential agrees with the potential measured using thin links for distances r/a ≥ 2. We calculated the lowest order perturbative expansion of the lattice Coulomb potential of HYP links. These results are used in analyzing the static potential both on quenched and dynamical lattices. The statistical accuracy of the potential with HYP links improves by about an order of magnitude, giving a reliable scale even with limited statistics both on quenched and dynamical lattices.

Dynamical twisted mass fermions with light quarks: simulation and analysis details

“…As a first, simple check on the possible impact of neglected NNLO terms on the results presented in Table 14, we have also included the heaviest point (the one at aµ q = 0.0150) in the standard fit to the formulae (39)- (40). In this case the results are still compatible with those in Table 14 within 1.7 standard deviations, but the χ 2 /d.o.f.…”

“…In this specific application of the bootstrap method the errorbars on the basic quantities am 2 PS and af PS are still needed, since the observables of interest, the low energy constants (LEC), are defined through minimization of the χ 2 of the simultaneous fit to the χPT formulae eqs. (39)- (40). Note that to safely employ the bootstrap method data need not have a Gaussian distribution, nor do the constraints, defined by the χPT formulae, need to be linear.…”

QCD with one compact spatial dimension

“…In all simulations the tadpole coefficient u 0 is fixed to a value of 0.875 for all simulations instead of determining it self-consistently at each value of β and am. In the scale setting runs we measure HYP smeared [24] Wilson loops to extract the hadronic scale r 0 [25] from the static quark potential [26] with results shown in Fig. 1.…”

Setting the scale for the Lüscher-Weisz action

“…We furthermore test the recently proposed method of hypercubic blocking [10] which was found [10,11] to improve the statistical accuracy in the determination of the static potential by an order of magnitude. We analyze quenched ensembles at 6 different values of the gauge coupling and compute the Sommer parameter [12,13] and the lattice spacing a.…”

“…This deviation is an effect of the hypercubic blocking. However, this effect can be computed perturbatively and the obtained deviation from the Coulomb potential is used to introduce a fourth fit parameter in the potential fit [11]. Subtracting this perturbative part gives the corrected data which we represent by bursts.…”