${\Lambda }_{\overline{\text{MS}}}^{(n_f=2)}$ from a momentum space analysis of the quark-antiquark static potential

Abstract

We determine ${\Lambda }_{\overline{\text{MS}}}^{(n_f=2)}$ by fitting perturbative expressions for the quark-antiquark static potential to lattice results for QCD with $n_f=2$ dynamical quark flavors. To this end we use the perturbative static potential at the presently best known accuracy, i.e. up to $\mathcal{O}({\alpha }_s^4)$, in momentum space. The lattice potential is computed on a fine lattice with $a\approx 0.042\text{fm}$ in position space. To allow for a comparison and matching of both results, the lattice potential is transformed into momentum space by means of a discrete Fourier transform. The value of ${\Lambda }_{\overline{\text{MS}}}^{(n_f=2)}$ is extracted in momentum space. All sources of statistical and systematic errors are discussed. The uncertainty in the value of ${\Lambda }_{\overline{\text{MS}}}^{(n_f=2)}$ is found to be smaller than that obtained in a recent position space analysis of the static potential based on the same lattice data.

arXiv comment30 pages, 6 figures; some clarifications added, matches journal version

References in corpus (64)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• The four-loop beta-function in Quantum Chromodynamics
• 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
• On the Viability of Lattice Perturbation Theory
• Chirally improving Wilson fermions - I. O(a) improvement
• Observation of String Breaking in QCD
• The static potential in QCD to two loops
• Strong Coupling Constant with Flavour Thresholds at Four Loops in the MS-bar Scheme
• Non-perturbative quark mass renormalization in quenched lattice QCD
• Thrust at N^3LL with Power Corrections and a Precision Global Fit for alphas(mZ)
• High-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
• A quark mass definition adequate for threshold problems
• The static quark-antiquark potential in QCD to three loops
• The ABM parton distributions tuned to LHC data
• Chirally improving Wilson fermions II. Four-quark operators
• The strange quark mass and Lambda parameter of two flavor QCD
• Three-loop static potential
• The infrared behaviour of the static potential in perturbative QCD
• Dynamical Twisted Mass Fermions with Light Quarks: Simulation and Analysis Details
• The static potential in QCD - a full Two-Loop Calculation
• Static QCD potential at three-loop order
• Light Meson Physics from Maximally Twisted Mass Lattice QCD
• Dynamical Twisted Mass Fermions with Light Quarks
• Determination of the bottom quark mass from the ${\rm Y}(1S)$ system
• Twisted mass lattice QCD
• Computation of the strong coupling in QCD with two dynamical flavours
• Chirally improving Wilson fermions
• Finite volume QCD at fixed topological charge
• QCD at Fixed Topology
• Fermionic contributions to the three-loop static potential
• The Running Coupling from SU(3) Lattice Gauge Theory
• An updated determination of α_s from tau decays
• A Determination of the Lambda Parameter from Full Lattice QCD
• Determination of alpha_s from the QCD static energy
• Determination of alpha_s from the QCD static energy: an update
• The Running Coupling from Lattice Gauge Theory
• Power corrections in the dispersive model for a determination of the strong coupling constant from the thrust distribution
• The static potential: lattice versus perturbation theory in a renormalon-based approach
• The QCD static energy at NNNLL
• Precise determination of the strong coupling constant in Nf=2+1 lattice QCD with the Schrödinger functional scheme
• Determination of the Static Potential with Dynamical Fermions
• Precision determination of r_0Lambda_MS from the QCD static energy
• Perturbative expansion of the QCD Adler function improved by renormalization-group summation and analytic continuation in the Borel plane
• Renormalons and confinement
• Ghost-gluon coupling, power corrections and ${\Lambda }_{\overline{\mathrm{MS}}}$ from twisted-mass lattice QCD at Nf=2
• The static-light meson spectrum from twisted mass lattice QCD
• High statistics determination of the strong coupling constant in Taylor scheme and its OPE Wilson coefficient from lattice QCD with a dynamical charm
• Lattice QCD with a chirally twisted mass term
• α_S from $F_{\pi }$ and Renormalization Group Optimized Perturbation
• RG/Pade Estimate of the Three-Loop Contribution to the QCD Static Potential Function
• Lambda_msbar from the static potential for QCD with n_f=2 dynamical quark flavors
• Violation of Casimir Scaling for Static QCD Potential at Three-loop Order
• Lattice study of vacuum polarization function and determination of strong coupling constant
• Lambda^{QCD}_{MS} from Renormalization Group Optimized Perturbation
• Quark-antiquark potential to order 1/m and heavy quark masses
• On the relation between QCD potentials in momentum and position space
• The Perturbative QCD Potential and the ttbar Threshold
• The infrared behavior of lattice QCD Green's functions
• Extracting hadron masses from fixed topology simulations
• Quark mass anomalous dimension and ${\Lambda }_{\overline{\text{MS}}}$ from the twisted mass Dirac operator spectrum
• Scale r_0 and the static potential from the CLS lattices
• QCD Lambda parameter from Landau-gauge gluon and ghost correlations
• Quark-antiquark static energy from a restricted Fourier transform
• Hadron masses from fixed topology simulations: parity partners and SU(2) Yang-Mills results

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• FLAG Review 2019
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• The QCD Running Coupling
• Transport Coefficients in Yang--Mills Theory and QCD
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• QCD Running Couplings and Effective Charges
• The chiral condensate from renormalization group optimized perturbation
• Colour field densities of the quark-antiquark excited flux tubes in SU(3) lattice QCD
• Importance of meson-meson and of diquark-antidiquark creation operators for a $\bar{b}\bar{b}ud$ tetraquark
• Determination of ${\Lambda }_{\overline{\text{MS}}}^{(n_f=2)}$ and analytic parameterization of the static quark-antiquark potential
• Lattice gauge theory computation of the static force
• The QCD Static Energy using Optimal Renormalization and Asymptotic Padé-approximant Methods
• QCD Static Force in Gradient Flow
• Quark mass anomalous dimension and ${\Lambda }_{\overline{\text{MS}}}$ from the twisted mass Dirac operator spectrum
• Eight very excited spectra and one possible axion in SU(3) lattice gauge theory
• Chiral Condensate and Spectral Density at full five-loop and partial six-loop orders of Renormalization Group Optimized Perturbation
• Spectrum of very excited ${\Sigma }_g^{+}$ flux tubes in SU(3) gauge theory
• Constructing static quark-anti-quark creation operators from Laplacian eigenmodes
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