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

*M. Bruno, M. Dalla Brida, P. Fritzsch, T. Korzec, S. Schaefer, A. Ramos, H. Simma, S. Sint, R. Sommer*

in 34th annual International Symposium on Lattice Field Theory

Contribution: pdf

**Abstract**

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.