Related papers: Advances in lattice hadron physics calculations us…
The gradient flow in QCD is treated perturbatively through next-to-next-to-leading order in the strong coupling constant. The evaluation of the relevant momentum and flow-time integrals is described, including various means of validation.…
We review recent lattice results for quark masses and low-energy hadronic parameters relevant for flavor physics. We do that by describing the FLAG initiative, with emphasis on its scope and rating criteria. The emerging picture is that…
A significant component of the cost of making predictions from lattice QCD stems from the computation of correlation functions on a given ensemble of gauge fields. This cost depends on the observable of interest and the details of its…
Perturbative calculations of gradient flow observables are technically challenging. Current results are limited to a few quantities and, in general, to low perturbative orders. Numerical stochastic perturbation theory is a potentially…
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…
The recent introduction of the gradient flow has provided a new tool to probe the dynamics of quantum field theories. The latest developments have shown how to use the gradient flow for the exploration of symmetries, and the definition of…
The gradient flow is the evolution of fields and physical quantities along a dimensionful parameter~$t$, the flow time. We give a simple argument that relates this gradient flow and the Wilsonian renormalization group (RG) flow. We then…
The Yang--Mills gradient flow has many interesting applications in lattice QCD. In this talk, some recent and possible future uses of the flow are discussed, emphasizing the underlying theoretical concepts rather than any computational…
This review concentrates on progress in lattice QCD during the last two years and, particularly, its impact on phenomenology. The two main technical developments have been successful implementations of lattice actions with exact chiral…
We consider extensions of the lattice gas model to incorporate radial flow. Experimental data are used to set the magnitude of radial flow. This flow is then included in the Lattice Gas Model in a microcanonical formalism. For magnitudes of…
It has become customary to use a smoothing algorithm called "gradient flow" to fix the lattice spacing in a simulation, through a parameter called $t_0$. It is shown that in order to keep the length $t_0$ fixed with respect to mesonic or…
We present a new family of relativistic lattice kinetic schemes for the efficient simulation of relativistic flows in both strongly-interacting (fluid) and weakly-interacting (rarefied gas) regimes. The method can also deal with both…
We develope a difference calculus analogous to the differential geometry by translating the forms and exterior derivatives to similar expressions with difference operators, and apply the results to fields theory on the lattice [Ref. 1]. Our…
The lattice regularization of QCD provides us with the most systematic way of computing non-perturbative properties of hadrons directly from the first principles of QCD. The recent rapid development of parallel computers has enabled us to…
The gradient flow exponentially suppresses ultraviolet field fluctuations and removes ultraviolet divergences (up to a multiplicative fermionic wavefunction renormalization). It can be used to describe real-space Wilsonian renormalization…
Our ability to resolve new physics effects is, largely, limited by the precision with which we calculate. The calculation of observables in the Standard (or a new physics) Model requires knowledge of associated hadronic contributions. The…
We report on the determination of the gradient flow scales in $N_f=2+1$ QCD using highly improved staggered quark (HISQ) ensembles generated by the HotQCD Collaboration for bare gauge couplings ranging from $\beta = 6.423$ to $8.400$. Using…
We describe in detail the implementation of a systematic perturbative approach to observables in the QCD gradient-flow formalism. This includes a collection of all relevant Feynman rules of the five-dimensional field theory and the…
Lattice Gauge Theory enables an ab initio study of the low-energy properties of Quantum Chromodynamics, the theory of the strong interaction. I begin these lectures by presenting the lattice formulation of QCD, and then outline the…
We report on a scale determination with gradient-flow techniques on the $N_f=2+1+1$ highly improved staggered quark ensembles generated by the MILC Collaboration. The ensembles include four lattice spacings, ranging from approximately 0.15…