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The $\Lambda$-parameter in 3-flavour QCD and $\alpha_s(m_Z)$ by the ALPHA collaboration

B. M., D.B. M., F. P., K. T, A. Ramos, S. S., S. H., S. S., S. R.

in 34th annual International Symposium on Lattice Field Theory

Contribution: pdf


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 $\Lambda_{\overline{\rm MS}}^{(3)} = 332(14)\,{\rm MeV}$ which translates to $\alpha_s(M_Z)=0.1179(10)(2)$ if one uses the standard perturbative procedure to match between 3-, 4- and 5-flavour QCD.