A New Way to Set the Energy Scale in Lattice Gauge Theories and its Application to the Static Force and ${\alpha }_s$ in SU(2) Yang--Mills Theory

Abstract

We introduce a hadronic scale $R_0$ through the force $F(r)$ between static quarks at intermediate distances $r$. The definition $F(R_0)R_0^2=1.65$ amounts to $R_0\simeq 0.5$~fm in phenomenological potential models. Since $R_0$ is well defined and can be calculated accurately in a Monte Carlo simulation, it is an ideal quantity to set the scale. In SU(2) pure gauge theory, we use new data (and $R_0$ to set the scale) to extrapolate $F(r)$ to the continuum limit for distances $r=0.18$~fm to $r=1.1$~fm. Through $R_0$ we determine the energy scale in the recently calculated running coupling, which used the recursive finite size technique to reach large energy scales. Also in this case, the lattice data can be extrapolated to the continuum limit. The use of one loop Symanzik improvement is seen to reduce the lattice spacing dependence significantly. Warning: The preprint is not completely fresh, but maybe you haven't seen it...

accepted in Nucl. Phys. B, 18 pages postscript-file with all figures

References in corpus (4)

• The Schrödinger Functional - a Renormalizable Probe for Non-Abelian Gauge Theories
• Computation of the Running Coupling in the SU(2) Yang-Mills Theory
• The Running Coupling from Lattice Gauge Theory
• SU(2) Potentials from Large Lattices

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• Spatial correlators in strongly coupled plasmas
• Unified chiral analysis of the vector meson spectrum from lattice QCD
• A Lattice Determination of Light Quark Masses
• A scaling study of the step scaling function in SU(3) gauge theory with improved gauge actions
• Fractional instanton of the SU($3$) gauge theory in weak coupling regime
• Lattice determinations of the strong coupling
• How perturbative are heavy sea quarks?
• Quark Hadron Duality at Finite Temperature
• SU(3) lattice gauge theory with a mixed fundamental and adjoint plaquette action: Lattice artefacts
• The Large $N_c$ limit of QCD on the lattice
• Spontaneous chiral symmetry breaking in QCD:a finite-size scaling study on the lattice
• Light hadron spectroscopy with two flavors of O(a) improved dynamical quarks
• The Polyakov loop at next-to-next-to leading order
• Lattice gauge theory computation of the static force
• Exotica and the Confining Flux
• Complex Langevin calculations in QCD at finite density
• Precision for B-meson matrix elements
• Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: $I=3/2$ $\pi K$ Scattering Length
• QCD with two dynamical flavors of chirally improved quarks
• Pseudoscalar Meson in Two Flavors QCD with the Optimal Domain-Wall Fermion
• Lattice Investigations of the Running Coupling
• Renormalization group invariant average momentum of non-singlet parton densities
• Overlap valence quarks on a twisted mass sea: a case study for mixed action Lattice QCD
• Quenched QCD with fixed-point and chirally improved fermion
• Heavy quark action on the anisotropic lattice
• Transition of $\rho \to \pi \gamma$ in Lattice QCD
• The Nc dependencies of baryon masses: Analysis with Lattice QCD and Effective Theory
• GMOR-like relation in IR-conformal gauge theories
• Heavy meson interquark potential
• Heavy Quark Physics and Lattice QCD
• Decay constants of P-wave heavy-light mesons from unquenched lattice QCD
• Non-perturbative renormalization of QCD
• Spin and orbital angular momentum of the proton
• Influence of topology on the scale setting
• Bosonic stringlike behavior and the Ultraviolet filtering of QCD
• Simulation of dynamical fermions with smeared links
• Sea quark effects in B_K from N_f=2 clover-improved Wilson fermions
• Lattice QCD at finite T and μ
• Strong coupling constant and quark masses from lattice QCD
• Form factors in lattice QCD
• Color flux tubes in $SU(3)$ Yang-Mills theory: an investigation with the connected correlator
• Past, present, and future of precision determinations of the QCD coupling from lattice QCD
• Study of QCD critical point using canonical ensemble method
• Topological Susceptibility on Dynamical Staggered Fermion Configurations
• Progress Towards finding Quark Masses and the QCD scale Lambda from the Lattice
• Large-order NSPT for lattice gauge theories with fermions: the plaquette in massless QCD
• Lattice QCD static potentials of the meson-meson and tetraquark systems computed with both quenched and full QCD
• Partial-Global Stochastic Metropolis Update for Dynamical Smeared Link Fermions
• The lattice scale at large beta in quenched QCD
• SU(3) Yang Mills theory at small distances and fine lattices
• Parallel Tempering in Lattice QCD with O(a)-Improved Wilson Fermions
• Two flavors of dynamical quarks on anisotropic lattices
• Exploring Topology Conserving Gauge Actions for Lattice QCD
• Testing improved staggered fermions with $m_s$ and $B_K$
• Tuning Actions and Observables in Lattice QCD
• Topological tunneling with Dynamical overlap fermions
• Lattice Monte-Carlo study of pre-conformal dynamics in strongly flavoured QCD in the light of the chiral phase transition at finite temperature
• A First Taste of Dynamical Fermions with an O(a) Improved Action
• Large cutoff effects of dynamical Wilson fermions
• Non-renormalizability of the HMC algorithm
• Scaling investigation of renormalized correlation functions in O(a) improved quenched lattice QCD
• Scale setting for large-$N$ SUSY Yang-Mills on the lattice
• Leptonic Decays of $B$- and $D$-Mesons
• Cutoff Effects on Energy-Momentum Tensor Correlators in Lattice Gauge Theory
• A new model for confinement
• Heavy Quarks on the Lattice
• Review on the determination of alpha_s from the QCD static energy
• Lattice calculations of the spectroscopy of baryons with broken flavor SU(3) symmetry and 3, 5, or 7 colors
• O(a) improved lattice QCD
• M_pi^2 versus m_q: comparing CP-PACS and UKQCD data to Chiral Perturbation Theory
• Themodynamics for pure SU($2$) gauge theory using gradient flow
• Continuum limit of hyperon vector coupling $f_1(0)$ from 2+1 flavor domain wall QCD
• Topological susceptibility in QCD with two flavors and 3-5 colors -- a pilot study
• Relativistic Quarkonia from Anisotropic Lattices
• The topological susceptibility and f_pi from lattice QCD
• Light Hadron Spectroscopy on Coarse Lattices with O(a^2) Mean-Field Improved Actions
• Suppressing dislocations in normalized hypercubic smearing
• Simple chromatic properties of gradient flow
• Static Energy in ($2+1+1$)-Flavor Lattice QCD: Scale Setting and Charm Effects
• Scalar and Tensor Glueballs on Asymmetric Coarse Lattices
• Continuum physics with quenched overlap fermions
• Strong coupling from non-equilibrium Monte Carlo simulations
• Quenched $B_K$-parameter from Osterwalder-Seiler tmQCD quarks and mass-splitting discretization effects
• Continuum extrapolation of energies of a four-quark system in lattice gauge theory
• Continuum Limit of Overlap Valence Quarks on a Twisted Mass Sea
• The QCD equation of state with 2+1 flavors of Highly Improved Staggered Quarks (HISQ)
• Gluonic profile of the static baryon at finite temperature
• Charmonium and bottomonium spectral functions in the vector channel
• Scale setting in lattice QCD
• Three-quark confinement potential from the Faddeev equation
• Dynamical Simulations with Smeared Link Staggered Fermions
• Wave Functions of the Proton Ground State in the Presence of a Uniform Background Magnetic Field in Lattice QCD
• Top-Down Holographic $G$-Structure Glueball Spectroscopy at (N)LO in $N$ and Finite Gauge Coupling
• A magnetic instability of the non-Abelian Sakai-Sugimoto model
• Finite temperature properties of QCD with two flavors and three, four and five colors
• Hadron masses from dynamical, non-perturbatively O(a) improved Wilson fermions
• Pion and kaon physics with improved staggered quarks
• The QCD Spectrum
• The (LATTICE) QCD Potential and Running Coupling: How to Accurately Interpolate between Multi-Loop QCD and the String Picture
• Glueball spectroscopy in lattice QCD using gradient flow
• Static forces in d=2+1 SU(N) gauge theories
• New results on cut-off effects in spectroscopy with the fixed point action
• Non-perturbative improvement of the axial current with three dynamical flavors and the Iwasaki gauge action
• Study of two color QCD on large lattices
• Streamlined data analysis in Python
• The negative-parity spin-1/2 $\Lambda$ baryon spectrum from lattice QCD and effective theory
• Light pseudoscalar meson masses and decay constants from mixed action lattice QCD
• A non-perturbative mechanism for elementary particle mass generation
• QCD bulk thermodynamics and conserved charge fluctuations with HISQ fermions
• 2+1 Flavor QCD simulated in the epsilon-regime in different topological sectors
• Spatial distributions in static heavy-light mesons: a comparison of quark models with lattice QCD
• Numerical study of tree-level improved lattice gradient flows in pure Yang-Mills theory
• Digitizing lattice gauge theories in the magnetic basis: reducing the breaking of the fundamental commutation relations
• Revisiting the flux tube spectrum of 3d SU(2) lattice gauge theory
• The shape of the static potential with dynamical fermions
• Mixed Action Simulations on Staggered Background; Interpretation and Result for the 2-flavor QCD Chiral Condensate
• Two loop mass effects in the static position space QCD-potential
• Lattice QCD with light Wilson quarks
• On the B*' --> B transition
• Verification of O(a) improvement
• Hard hadron spectroscopy
• Comparing topological charge definitions using topology fixing actions
• Testing chiral effective theory with quenched lattice QCD
• The Wilson Flow and the finite temperature phase transition
• On the equivalence between the Wilson flow and stout-link smearing
• Heavy-light decay constants with three dynamical flavors
• Born-Oppenheimer Potentials for $SU(3)$ Gauge Theory
• A quenched study of the Schroedinger functional with chirally rotated boundary conditions: applications
• Dynamical twisted mass fermions
• SUSY Higgs Mass and Collider Signals with a Hidden Valley
• Can holography reproduce the QCD Wilson line?
• Hybrid configuration content of heavy S-wave mesons
• Noise reduction algorithm for Glueball correlators
• Hadron Structure in Lattice QCD
• On the $N_f$-dependence of gluonic observables
• Phenomenology of renormalons and the OPE from lattice regularization: the gluon condensate and the heavy quark pole mass
• Five-Dimensional Gauge-Higgs Unification: A Standard Model-Like Spectrum
• The charm quark's mass in quenched QCD
• Setting the scale for nHYP fermions with the Lüscher-Weisz gauge action
• Lattice $B$-field correlators for heavy quarks
• Determining Lines of Constant Physics in the Confinement Phase of the SU(2) Higgs Model
• SU(3) glueballs on coarse, anisotropic lattices
• Perturbative and non-perturbative studies of the SU(2)-Higgs model on lattices with asymmetric lattice spacings
• String breaking and lines of constant physics in the SU(2) Higgs model
• Exploring gauge theories with adjoint matter on the lattice
• Fixed Point SU(3) Gauge Actions: Scaling Properties and Glueballs
• Mass spectrum of $2$-dimensional $\mathcal{N}=(2,2)$ super Yang-Mills theory on the lattice
• Preparing for N_f=2 simulations at small lattice spacings
• Pressure and interaction measure of the gluon plasma
• Structure of the ${\Omega }^{-}(2012)$ with Hamiltonian Effective Field Theory
• Approximate actions for dynamical fermions
• QCD with dynamical Wilson fermions - first results from SESAM
• Two Lectures on QCD at Short Distances: Jets and Factorization
• Constructing static quark-anti-quark creation operators from Laplacian eigenmodes
• Scale Determination Using the Static Potential with Two Dynamical Quark Flavors
• Non-perturbative renormalization of tensor currents: strategy and results for $N_f=0$ and $N_f=2$ QCD
• Continuum extrapolation of the gradient-flowed color-magnetic correlator at $1.5T_c$
• Discretisation effects in the topological susceptibility in lattice QCD
• One-loop lattice artifacts of a dynamical charm quark
• Classically Perfect Gauge Actions on Anisotropic Lattices
• Brief Review of Saturation Physics
• $b\bar{b}$ Description with a Screened Potential
• Scaling of gauge balls and static potential in the confinement phase of the pure U(1) lattice gauge theory
• An Improved Single-Plaquette Gauge Action
• $B_s\to K\ell \nu$ form factors with 2+1 flavors
• Static quark anti-quark interactions at non-zero temperature from lattice QCD
• The complete lowest order chiral Lagrangian from a little box
• Confinement, the gluon propagator and the interquark potential for heavy mesons
• Update on the Sea Contributions to Hadron Electric Polarizabilities through Reweighting
• Static force from generalized Wilson loops on the lattice using the gradient flow
• Zero Temperature String Breaking with Staggered Quarks
• Quark mass dependence of quarkonium properties at finite temperature
• Quarkonium and hydrogen spectra with spin dependent relativistic wave equation
• Running coupling constant and correlation length from Wilson loops
• New lessons from the nucleon mass, lattice QCD and heavy baryon chiral perturbation theory
• Study of the Roberge-Weiss phase caused by external uniform classical electric field using lattice QCD approach
• Semileptonic Decays of D and B Mesons
• Sum Rules and Cutoff Effects in Wilson Lattice QCD
• A new lattice measurement for potentials between static SU(3) sources
• Determining fundamental parameters of QCD on the lattice
• Relative scale setting for two-color QCD with Nf=2 Wilson fermions
• Static Potential in the SU(2)-Higgs Model and Coupling Constant Definitions in Lattice and Continuum Models
• A novel method for the physical scale setting on the lattice and its application to $N_f$=4 simulations
• Induced QCD I: Theory
• Heavy tetraquark confining potential in Coulomb gauge QCD
• The Heavy Hadron Spectrum
• Lattice Perturbation Theory
• Magnetic Polarisability of Octet Baryons via Lattice QCD
• Spectroscopy of SU(4) lattice gauge theory with fermions in the two index anti-symmetric representation
• $\mathcal{N}=1$ Super-Yang-Mills theory on the lattice with twisted mass fermions
• A lattice Dirac operator for QCD with light dynamical quarks
• Non Perturbative One Gluon Exchange Potential from Dyson-Schwinger Equations
• Color-Coulomb Force Calculated from Lattice Coulomb Hamiltonian
• Charm quark effects on the strong coupling extracted from the static force
• Heavy-strange meson decay constants in the continuum limit of quenched QCD
• Confining potential under the gauge field condensation in the SU(2) Yang-Mills theory
• Matching Lagrangian and Hamiltonian Simulations in (2+1)-dimensional U(1) Gauge Theory
• Localization of topological charge density near $T_c$ in quenched QCD with Wilson flow
• Large $N$ scaling and factorization in SU($N$) Yang-Mills gauge theory
• Induced QCD II: Numerical results
• Universality and RG-improved gauge actions
• QCD-Instantons at HERA -- An Introduction
• Two-dimensional $\mathcal{N}=2$ Super-Yang-Mills Theory
• Light hadron spectroscopy with O(a) improved dynamical fermions
• Decoupling of charm beyond leading order
• Particle yields from numerical simulations
• Approaching the conformal window: systematic study of the particle spectrum in SU(2) field theory with Nf=2, 4 and 6
• Non-perturbative renormalization of the axial current with improved Wilson quarks
• Vector correlator and scale determination in lattice QCD
• Quenching Effects in the Hadron Spectrum
• Four Quarks from Lattice to the Continuum
• Modifying the molecular dynamics action to increase topological tunnelling rate for dynamical overlap fermions
• The one-flavor quark condensate and related problems
• Light dynamical fermions on the lattice: toward the chiral regime of QCD
• Spatial string tension in $N_f=2$ lattice QCD at finite temperature
• Spontaneous breaking of discrete symmetries in QCD on a small volume
• Exploiting the hopping parameter expansion in the hybrid Monte Carlo (HMC) simulation of lattice QCD with two degenerate flavours of Wilson fermions
• Numerical study of staggered fermion on anisotropic lattices
• Anisotropic lattices for precision computations in heavy flavor physics
• Euclidean correlation functions of the topological charge density
• Flavour-singlet pseudoscalar and scalar mesons
• The topological susceptibility in `full' (UK)QCD
• UKQCD's latest results for the static quark potential and light hadron spectrum with O(a) improved dynamical fermions
• Topology of trace deformed Yang-Mills theory
• Super-heavy Quarkonia as a probe of the QCD Vacuum
• Split of the pseudo-critical temperatures of chiral and confine/deconfine transitions by temperature gradient
• Strings of diquark-quark (QQ)Q baryon before phase transition
• Meson spectrum in the large $N$ limit
• Running coupling constant and correlation length from Wilson loops
• Shear and bulk viscosities of the gluon plasma across the transition temperature from lattice QCD
• Determination of constant lattice spacing trajectories in lattice QCD
• Topological susceptibility and excess kurtosis in SU(3) Yang-Mills theory
• The determination of potential scales in 2+1 flavor QCD
• Thermal modifications of charmonia and bottomonia from spatial correlation functions
• Application of top-down holographic thermal QCD at finite coupling
• How to Accurately Extract the Running Coupling of QCD from Lattice Potential Data
• The static quark potential in 2+1 flavour Domain Wall QCD from QCDOC
• Lattice QCD with light dynamical quarks
• Excited States of the Nucleon in 2+1 Flavor QCD
• Memory efficient finite volume schemes with twisted boundary conditions
• Scaling and Luescher Term in a non-Abelian (2+1)d SU$(2)$ Quantum Link Model
• Wilson loops with neural networks
• Static potential in the SU(2) Higgs model
• Hadron masses: lattice QCD and chiral effective field theory
• Quark Loop Effects with an Improved Staggered Action
• The N_f=0 heavy quark potential and perturbation theory
• Novel Approaches to Renormalization Group Transformations in the Continuum and on the Lattice
• Investigating some technical improvements to glueball calculations
• Lattice QCD with Dynamical Quarks from the UKQCD Collaboration
• String/$\mathcal{M}$-theory Dual of Large-$N$ Thermal QCD-Like Theories at Intermediate Gauge/'t Hooft Coupling and Holographic Phenomenology
• Novel insight into centre-vortex geometry in four dimensions
• Dynamical fermions in lattice quantum chromodynamics
• Remarks on the discretization of physical momenta in lattice QCD
• Effects of Dynamical Quarks in UKQCD Simulations
• Background field and time dependence effects in holographic models