The determination of $\hat{I}{\pm }_s$ by the ALPHA collaboration

Abstract

We review the ALPHA collaboration strategy for obtaining the QCD coupling at high scale. In the three-flavor effective theory it avoids the use of perturbation theory at $\hat{I}\pm >0.2$ and at the same time has the physical scales small compared to the cutoff $1/a$ in all stages of the computation. The result $Λ_\overline{MS}^{(3)}=332(14)$~MeV is translated to $α_\overline{MS}(m_Z)=0.1179(10)(2)$ by use of (high order) perturbative relations between the effective theory couplings at the charm and beauty quark "thresholds". The error of this perturbative step is discussed and estimated as $0.0002$.

7 pages, proceedings of FPCapri2016 conference