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

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Cited by in corpus (7)

• Towards the phase diagram of dense two-color matter
• QCD thermodynamics with dynamical overlap fermions
• The Yang-Mills gradient flow in finite volume
• The gradient flow running coupling scheme
• Anisotropy tuning with the Wilson flow
• Status and challenges of simulations with dynamical fermions
• MCRG study of 8 and 12 fundamental flavors