Abstract
A high precision determination of the strong coupling constant in the MS scheme at the Z-mass scale, using low energy quantities, namely pion/kaon decay constants and masses, as experimental input is presented. The computation employs two different massless finite volume renormalization schemes to non-perturbatively trace the scale dependence of the respective running couplings from a scale of about 200 MeV to 100 GeV. At the largest energies perturbation theory is reliable. At high energies the Schrödinger-Functional scheme is used, while the running at low and intermediate energies is computed in a novel renormalization scheme based on an improved gradient flow. Large volume Nf = 2 + 1 QCD simulations by CLS are used to set the overall scale. The result is compared to world averages by FLAG and the PDG.
Highlights
Parameters of the standard model have to be determined experimentally before any predictions can be made
At high energies the Schrödinger-Functional scheme is used, while the running at low and intermediate energies is computed in a novel renormalization scheme based on an improved gradient flow
The main uncertainties are systematic errors associated with the necessary processing of the raw data, before it can be compared to perturbation theory
Summary
Parameters of the standard model have to be determined experimentally before any predictions can be made. To infer what fundamental process has taken place from the measured energies and momenta of photons, leptons and hadrons, one relies on a detailed mathematical model of the detector, and on a good understanding of the hadronization process The latter is too complicated to be computed within the standard model and various model assumptions enter which in the end may dominate the systematic error. For instance the most recent result [7] of Fig. 1 uses lattices with up to L/a = 64 sites, renormalization scales μ ≈ 5 GeV with lattice spacings a−1 ≈ 3.3 GeV and coarser These systematic errors can be nearly eliminated by switching to finite volume renormalization schemes [8], where μ ≡ L−1.
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