Volume 256 -
34th annual International Symposium on Lattice Field Theory (LATTICE2016) -
Standard Model Parameters and Renormalization

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

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Pre-published on:
2017 February 14

Published on:
2017 March 24

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.

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