High-precision scale setting in lattice QCD

Abstract

Scale setting is of central importance in lattice QCD. It is required to predict dimensional quantities in physical units. Moreover, it determines the relative lattice spacings of computations performed at different values of the bare coupling, and this is needed for extrapolating results into the continuum. Thus, we calculate a new quantity, $w_0$, for setting the scale in lattice QCD, which is based on the Wilson flow like the scale $t_0$ (M. Luscher, JHEP 1008 (2010) 071). It is cheap and straightforward to implement and compute. In particular, it does not involve the delicate fitting of correlation functions at asymptotic times. It typically can be determined on the few per-mil level. We compute its continuum extrapolated value in 2+1-flavor QCD for physical and non-physical pion and kaon masses, to allow for mass-independent scale setting even away from the physical mass point. We demonstrate its robustness by computing it with two very different actions (one of them with staggered, the other with Wilson fermions) and by showing that the results agree for physical quark masses in the continuum limit.

15 pages, 7 figures, 2 tables; Version published in JHEP

References in corpus (31)

• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• The QCD equation of state with dynamical quarks
• 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
• The QCD transition temperature: results with physical masses in the continuum limit
• Is there still any Tc mystery in lattice QCD? Results with physical masses in the continuum limit III
• Properties and uses of the Wilson flow in lattice QCD
• The Chroma Software System for Lattice QCD
• Ab-initio Determination of Light Hadron Masses
• Flavor Symmetry and the Static Potential with Hypercubic Blocking
• Analytic Smearing of SU(3) Link Variables in Lattice QCD
• The QCD transition temperature: results with physical masses in the continuum limit II.
• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Fluctuations of conserved charges at finite temperature from lattice QCD
• Trivializing maps, the Wilson flow and the HMC algorithm
• Infinite N phase transitions in continuum Wilson loop operators
• Monte Carlo errors with less errors
• High Precision determination of the pi, K, D and D_s decay constants from lattice QCD
• High-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
• Continuum Limit Physics from 2+1 Flavor Domain Wall QCD
• The QCD phase diagram at nonzero quark density
• B- and D-meson decay constants from three-flavor lattice QCD
• Lattice QCD at the physical point: Simulation and analysis details
• Lattice QCD at the physical point: light quark masses
• Lattice QCD as a video game
• The static quark potential in three flavor QCD
• Precise determination of the lattice spacing in full lattice QCD
• Precision computation of the kaon bag parameter
• Rationale for UV-filtered clover fermions
• The ratio FK/Fpi in QCD
• Scaling study of dynamical smeared-link clover fermions
• Determination of the Static Potential with Dynamical Fermions

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