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We review the ALPHA collaboration strategy for obtaining the QCD coupling at high scale. In the three-flavor effective theory it avoids the use of perturbation theory at α∼>0.2and at the same time has the physical scales small compared to the cutoff 1/ain all stages of the computation. The result ΛMS‾(3)=332(14)MeVis translated to αMS‾(mZ)=0.1179(10)(2)by use of (high order) perturbative relations between the effective theory couplings at the charm and beauty quark “thresholds”. The error of this perturbative step is discussed and estimated as 0.0002.

Abstract: Worm algorithms have been very successful with the simulation of sigma models with fixed length spins which result from scalar field theories in the limit of infinite quartic coupling λ. Here we investigate closer their algorithmic efficiency at finite and even vanishing λ for the one component model in dimensions . [Copyright &y& Elsevier]

We present measurements of a combination of the decay constants of the light pseudoscalar mesons and the gradient flow scale t0, which allow us to set the scale of the lattices generated by CLS with 2+1 flavors of nonperturbatively improved Wilson fermions. Mistunings of the quark masses are corrected for by measuring the derivatives of observables with respect to the bare quark masses. [ABSTRACT FROM AUTHOR]

We present a lattice QCD calculation of the ∆(1232) matrix elements of the axial-vector and pseudoscalar currents. The decomposition of these matrix elements into the appropriate Lorentz invariant form factors is carried out, and the techniques to calculate the form factors are developed and tested using quenched configurations. Results are obtained for 2 + 1 domain wall fermions and within a hybrid scheme with domain wall valence and staggered sea quarks. Two Goldberger-Treiman-type relations connecting the axial to the pseudoscalar effective couplings are derived. These and further relations based on the pionpole dominance hypothesis are examined using the lattice QCD results, finding support for their validity. Using lattice QCD results on the axial charges of the nucleon and the A, as well as the nucleon-to-∆ transition coupling constant, we perform a combined chiral fit to all three quantities and study their pion mass dependence as the chiral limit is approached. [ABSTRACT FROM AUTHOR]

We study the two dimensional XY-model with high precision Monte Carlo techniques and investigate the continuum approach of the step-scaling function of its finite volume mass gap. The continuum extrapolated results are found consistent with analytic predictions for the finite volume energy spectrum based on the equivalence with sine-Gordon theory. To come to this conclusion it was essential to use an also predicted form of logarithmic decay of lattice artifacts for the extrapolation. [Copyright &y& Elsevier]

Using a finite volume gradient flow renormalization scheme with Schrödinger Functional boundary conditions, we compute the nonperturbative running coupling in the range 2.2≲gGF-2(L)≲13. Careful continuum extrapolations turn out to be crucial to reach our high accuracy. The running of the coupling is always between one loop and two loop and very close to one loop in the region of 200 MeV≲μ=1/L≲4 GeV. While there is no convincing contact to two-loop running, we match nonperturbatively to the Schrödinger functional coupling with background field. In this case, we know the μ-dependence up to ∼100 GeV and can thus connect to the Λ-parameter. [ABSTRACT FROM AUTHOR]