Related papers: The lattice gradient flow at tree level
The static QCD force from the lattice can be used to extract $\Lambda_{\overline{\textrm{MS}}}$, which determines the running of the strong coupling. Usually, this is done with a numerical derivative of the static potential. However, this…
The one-loop determination of the coefficient $c_\text{SW}$ of the Wilson quark action has been useful to push the leading cut-off effects for on-shell quantities to $\mathcal{O}(\alpha^2 a)$ and, in conjunction with non-perturbative…
When designing lattice actions, gauge field smearing is often used in the definition of the lattice Dirac operator. Too much smearing can result in uncontrolled continuum extrapolations as the short distance behaviour of the theory is…
We investigate properties of the topological charge for several SU(NC) gauge field ensembles for NC = 4, 5, 6 with a single fermion in the two-index anti-symmetric representation, covering multiple lattice spacings at otherwise…
We use gradient flow to compute the static force based on a Wilson loop with a chromoelectric field insertion. The result can be compared on one hand to the static force from the numerical derivative of the lattice static energy, and on the…
Lattice calculations of hadronic observables are aggravated by short-distance fluctuations. The gradient flow, which can be viewed as a particular realisation of the coarse-graining step of momentum space RG transformations, proves a…
We perform the scale setting procedure of a mixed action setup consisting of valence Wilson twisted mass fermions at maximal twist on CLS ensembles with $N_f=2+1$ flavours of $O(a)$-improved Wilson sea quarks. We determine the gradient flow…
Lattice scales defined using gradient flow are typically very precise, while also easy to calculate. However, different definitions of flows and operators can differ significantly, suggesting possible systematical effects. Using a subset of…
We calculate the third coefficient of the lattice beta function in QCD with Wilson fermions, extending the pure gauge results of Luescher and Weisz; we show how this coefficient modifies the scaling function on the lattice. We also…
We investigate the discrete $\beta$ function of the 2-flavor SU(3) sextet model using the finite volume gradient flow scheme. Our results, using clover improved nHYP smeared Wilson fermions, follow the (non-universal) 4-loop…
When designing lattice actions, gauge field smearing is frequently used to define the lattice Dirac operator. Since the smearing procedure removes effects of ultraviolet fluctuations, the fermions effectively see a larger lattice spacing…
The step-scaling function, the lattice analog of the renormalization group $\beta$ function, is presented for the SU(3) gauge system with eight flavors in the fundamental representation. Our investigation is based on generating dynamical…
The Yang-Mills gradient flow is considered on the four dimensional torus T^4 for SU(N) gauge theory coupled to N_f flavors of massless fermions in arbitrary representations. The small volume dynamics is dominated by the constant gauge…
We apply the gradient flow on a color-electric two-point function that encodes the heavy quark momentum diffusion coefficient. The simulations are done on fine isotropic lattices in the quenched approximation at $1.5\,T_c$. The continuum…
We calculate the step scaling function, the lattice analog of the renormalization group $\beta$-function, for an SU(3) gauge theory with twelve flavors. The gauge coupling of this system runs very slowly, which is reflected in a small step…
We present a precise computation of the topological charge distribution in the $SU(3)$ Yang-Mills theory. It is carried out on the lattice with high statistics Monte Carlo simulations by employing the clover discretization of the field…
We present a new lattice study of the discrete beta function for SU(3) gauge theory with Nf=8 massless flavors of fermions in the fundamental representation. Using the gradient flow running coupling, and comparing two different nHYP-smeared…
We consider spectral quantities in lattice QCD and determine the asymptotic behavior of their discretization errors. Wilson fermion with O$(a)$-improvement, (M\"obius) Domain wall fermion (DWF), and overlap Dirac operators are considered in…
We study several types of tree-level improvement in the Yang-Mills gradient flow method in order to reduce the lattice discretization errors in line with Fodor et al. [arXiv:1406.0827]. The tree-level $\mathcal{O}(a^2)$ improvement can be…
In this paper we investigate the cutoff effects at tree-level of perturbation theory for three different lattice regularizations of fermions -- maximally twisted mass Wilson, overlap and Creutz fermions. We show that all three kinds of…