Journal of High Energy Physics

, 2012:10 | Cite as

High-precision scale setting in lattice QCD

  • Budapest-Marseille-Wuppertal collaboration
  • Szabolcs BorsányiEmail author
  • Stephan Dürr
  • Zoltán Fodor
  • Christian Hoelbling
  • Sándor D. Katz
  • Stefan Krieg
  • Thorsten Kurth
  • Laurent Lellouch
  • Thomas Lippert
  • Craig McNeile
  • Kálmán K. Szabó
Open Access


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 08 (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.


Lattice QCD Lattice Gauge Field Theories 

Supplementary material

13130_2012_4694_MOESM1_ESM.c (23 kb)
ESM 1 (C 23 kb)
13130_2012_4694_MOESM2_ESM.c (60 kb)
ESM 2 (C 59 kb)


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Copyright information

© SISSA 2012

Authors and Affiliations

  • Budapest-Marseille-Wuppertal collaboration
  • Szabolcs Borsányi
    • 1
    Email author
  • Stephan Dürr
    • 1
    • 2
  • Zoltán Fodor
    • 1
    • 2
    • 3
  • Christian Hoelbling
    • 1
  • Sándor D. Katz
    • 3
  • Stefan Krieg
    • 1
    • 2
  • Thorsten Kurth
    • 1
  • Laurent Lellouch
    • 4
  • Thomas Lippert
    • 1
    • 2
  • Craig McNeile
    • 1
  • Kálmán K. Szabó
    • 1
  1. 1.Bergische Universität WuppertalWuppertalGermany
  2. 2.Jülich Supercomputing CentreJülichGermany
  3. 3.Institute for Theoretical PhysicsEötvös UniversityBudapestHungary
  4. 4.Centre de Physique Théorique, CNRS, Aix-Marseille U. and U. Sud Toulon-VarMarseilleFrance

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