High-precision scale setting in lattice QCD

By S. Borsányi, S. Dürr, Zoltán Fodor, Christian Hoelbling, Sándor D. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, Craig McNeile and 2 more. 2012

343 citations recorded by the source corpus.

A bstractScale 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, w0, for setting the scale in lattice QCD, which is based on the Wilson flow like the scale t0 (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.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ca5d2c6c0c6322c05ce1d1b57b20258a30f88d32

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In Nuclear and High Energy Physics

Citations in the corpus

Heavy quarkonium in extreme conditions (2019, methodology): “More recently a different high precision scale setting approach [75] has been developed based on the Gradient flow technique [76].”
Setting the scale for the CLS 2 +1 flavor ensembles (2016, result): “This compares well to previous determinations using 2þ 1 flavors by the BMW collaboration [33] that quotes ffiffiffiffiffiffi 8t0 p 1⁄4 0.”
Simulation of QCD with Nf = 2 + 1 flavors of non-perturbatively improved Wilson fermions (2014, methodology): “4144(59)(37) fm by the BMW collaboration using Nf =2+1 flavors [29].”
Scale Setting in Lattice QCD (2014, methodology): “heory estimates are just indicative. While these are no particularly large cutoff effects, one may be interested in reducing them by Symanzik improvement and indeed, the Symanzik ﬂow has been used in [33, 34]. “Symanzik ﬂow” refers to the ﬂow equation, continuous in t, but with the gradient on the r”
The Yang-Mills gradient flow in finite volume (2012, methodology): “Both the discretization in [3] and also the tree level improved Symanzik discretization of [7] was measured.”
FLAG Review 2019 (2019, methodology): “15 fm, scale set with fπ+ and relative scale set with the Wilson flow [271, 272]) supplemented by some simulation points with heavier quark masses.”
Fundamental composite dynamics: A review (2020, methodology): “The scale was set by using the w0 observable [95] and the RI-MOM scheme [96] was used to measure the required nonperturbative renomalization constants.”
Leading hadronic contribution to the muon magnetic moment from lattice QCD (2020, methodology): “tely to the operator VIII, drawn with a solid line. accuracy better than a permil level. The mass M satises all three criteria, see Section 4 for more details. In this work we also use the w 0-scale [6], which is derived from the Wilsonow of the gauge elds [7]. The main motivation for this scale set”
Review of lattice results concerning low-energy particle physics (2016, methodology): “15 fm, scale set with fπ+ and relative scale set with the Wilson flow [245,246]) supplemented by some simulation points with heavier quark masses.”