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

TL;DR

This paper reports precise lattice QCD calculations of the $\\Lambda$-parameter and the strong coupling constant $\alpha_s(m_Z)$, connecting theoretical predictions with experimental hadronic data to improve understanding of strong interactions.

Contribution

The paper provides a new determination of the $\Lambda$-parameter in 3-flavour QCD and $\alpha_s(m_Z)$ using lattice simulations and experimental decay constants, refining previous results.

Findings

$\Lambda_{\overline{\rm MS}}^{(3)} = 332(14)$ MeV

$\alpha_s(M_Z)=0.1179(10)(2)$

Consistent matching between 3-, 4-, and 5-flavour QCD

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 $\Lambda_{\overline{\rm MS}}^{(3)} = 332(14)$ MeV which translates to $\alpha_s(M_Z)=0.1179(10)(2)$ using perturbation theory to match between 3-, 4- and 5-flavour QCD.