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تسجيل مستخدم جديدA status update on the determination of ${Lambda}_{overline{rm MS}}^{N_{rm f}=3}$ by the ALPHA collaboration
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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 $L_{rm max} F_K$.
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