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Register a new userThe $Lambda$-parameter in 3-flavour QCD and $alpha_s(m_Z)$ by the ALPHA collaboration
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We present results by the ALPHA collaboration for the $Lambda$-parameter in 3-flavour QCD and the strong coupling constant at the electroweak scale, $alpha_s(m_Z)$, in terms of hadronic quantities computed on the CLS gauge configurations. The first part of this proceedings contribution contains a review of published material cite{Brida:2016flw,DallaBrida:2016kgh} and yields the $Lambda$-parameter in units of a low energy scale, $1/L_{rm had}$. We then discuss how to determine this scale in physical units from experimental data for the pion and kaon decay constants. We obtain $Lambda_{overline{rm MS}}^{(3)} = 332(14)$ MeV which translates to $alpha_s(M_Z)=0.1179(10)(2)$ using perturbation theory to match between 3-, 4- and 5-flavour QCD.
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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 $alpha > 0.2$ and at the same time has the physical scales small compared to the cutoff $1/a$ in all stages of the computation. The result $Lambda_overline{MS}^{(3)}=332(14)$~MeV is translated to $alpha_overline{MS}(m_Z)=0.1179(10)(2)$ 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 $0.0002$.
We determine f_K for lattice QCD in the two flavor approximation with non-perturbatively improved Wilson fermions. The result is used to set the scale for dimensionful quantities in CLS/ALPHA simulations. To control its dependence on the light quark mass, two different strategies for the chiral extrapolation are applied. Combining f_K and the bare strange quark mass with non-perturbative renormalization factors and step scaling functions computed in the Schroedinger Functional, we determine the RGI strange quark mass and the Lambda parameter in units of f_K.
We revisit the earlier determination of alpha_s(M_Z) via perturbative analyses of short-distance-sensitive lattice observables, incorporating new lattice data and performing a modified version of the original analysis. We focus on two high-intrinsic-scale observables, log(W_11) and log(W_12), and one lower-intrinsic scale observable, log(W_{12}/u_0^6), finding improved consistency among the values extracted using the different observables and a final result, alpha_s(M_Z)=0.1192(11), 2 sigma higher than the earlier result, in excellent agreement with recent non-lattice determinations and, in addition, in good agreement with the results of a similar, but not identical, re-analysis by the HPQCD Collaboration. A discussion of the relation between the two re-analyses is given, focussing on the complementary aspects of the two approaches.
The ALPHA collaboration aims to determine $alpha_s(m_Z)$ with a total error below the percent level. A further step towards this goal can be taken by combining results from the recent simulations of 2+1-flavour QCD by the CLS initiative with a number of tools developed over the years: renormalized couplings in finite volume schemes, recursive finite size techniques, two-loop renormalized perturbation theory and the (improved) gradient flow on the lattice. We sketch the strategy, which involves both the standard SF coupling in the high energy regime and a gradient flow coupling at low energies. This implies the need for matching both schemes at an intermediate switching scale, $L_{rm swi}$, which we choose roughly in the range 2-4 GeV. In this contribution we present a preliminary result for this matching procedure, and we then focus on our almost final results for the scale evolution of the SF coupling from $L_{rm swi}$ towards the perturbative regime, where we extract the $N_{rm f} = 3$ ${Lambda}$-parameter, ${Lambda}_{overline{rm MS}}^{N_{rm f}=3}$, in units of $L_{rm swi}$ . Connecting $L_{rm swi}$ and thus the ${Lambda}$-parameter to a hadronic scale such as $F_K$ requires 2 further ingredients: first, the connection of $L_{rm swi}$ to $L_{rm max}$ using a few steps with the step-scaling function of the gradient flow coupling, and, second, the continuum extrapolation of $L_{rm max} F_K$.
The LatKMI collaboration is studying systematically the dynamical properties of N_f = 4,8,12,16 SU(3) gauge theories using lattice simulations with (HISQ) staggered fermions. Exploring the spectrum of many-flavour QCD, and its scaling near the chiral limit, is mandatory in order to establish if one of these models realises the Walking Technicolor scenario. Although lattice technologies to study the mesonic spectrum are well developed, scalar flavour-singlet states still require extra effort to be determined. In addition, gluonic observables usually require large-statistic simulations and powerful noise-reduction techniques. In the following, we present useful spectroscopic methods to investigate scalar glueballs and scalar flavour-singlet mesons, together with the current status of the scalar spectrum in N_f = 12 QCD from the LatKMI collaboration.
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