Lattice QCD at the physical point: simulation and analysis details

By S. Dürr, Zoltán Fodor, Christian Hoelbling, Sándor D. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, Kálmán K. Szabó, G. Vulvert and 1 more. 2010

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We give details of our precise determination of the light quark masses mud = (mu + md)/2 and ms in 2 + 1 flavor QCD, with simulated pion masses down to 120 MeV, at five lattice spacings, and in large volumes. The details concern the action and algorithm employed, the HMC force with HEX smeared clover fermions, the choice of the scale setting procedure and of the input masses. After an overview of the simulation parameters, extensive checks of algorithmic stability, autocorrelation and (practical) ergodicity are reported. To corroborate the good scaling properties of our action, explicit tests of the scaling of hadron masses in Nf = 3 QCD are carried out. Details of how we control finite volume effects through dedicated finite volume scaling runs are reported. To check consistency with SU(2) Chiral Perturbation Theory the behavior of Mπ2/mud and Fπ as a function of mud is investigated. Details of how we use the RI/MOM procedure with a separate continuum limit of the running of the scalar density RS(μ, μ′) are given. This procedure is shown to reproduce the known value of r0ms in quenched QCD. Input from dispersion theory is used to split our value of mud into separate values of mu and md. Finally, our procedure to quantify both systematic and statistical uncertainties is discussed.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/445d7cbfff7b571c3e2c18ef5d0b3d2761907437

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Scale Setting in Lattice QCD (2014, background): “uark mass extra/interpolations, even though this is rather relevant. I just note that precisions quoted for m W (usually after the extrapolation to the physical point) are ˇ0:5 % [11], ˇ1 % [10], ˇ1% [37], ˇ5 % [13]. Obviously, such numbers depend on the statistics. Nowadays it is typically around 1”
Review of lattice results concerning low-energy particle physics (2016, methodology): “They obtain ms by combining that value of mc/ms with already existing phenomenological calculations of mc. Subsequently they obtain mud by combining this result for ms with the Nf = 2+1 calculation ofms/mud of BMW 10A, 10B [7, 8] discussed below.”
High-precision scale setting in lattice QCD (2012, methodology): “erent pion mass cuts in the M -ts, i.e. M ˇ < 380MeV;480MeV). Each of these analyses can be fully justied and can be considered \the" nal analysis. Thus, according to our standard procedure [14,16,25,32], we construct a histogram out of the values obtained for w 0, where each one is weighted”
The mass spectrum of the Schwinger model with matrix product states (2013, methodology): “n ﬁtting interval in x. To take this systematic uncertainty into account, we perform the following error analysis procedure, similar to those employed in data analysis for Lattice QCD (see e.g. Refs. [54, 55]). Let us assume that, for a ﬁxed value of m/g, we have a set of data for the chosen observa”