The determination of $\alpha_s$ by the ALPHA collaboration

TL;DR

The ALPHA collaboration determines the strong coupling constant $oldsymbol{ ext{alpha}_s}$ at high energy scales using a non-perturbative lattice QCD approach, achieving precise results with controlled errors and minimal reliance on perturbation theory.

Contribution

This work presents a novel non-perturbative method for calculating $oldsymbol{ ext{alpha}_s}$ at high scales, reducing perturbative uncertainties in the process.

Findings

$oldsymbol{ ext{Lambda}}_{ ext{MS}}^{(3)}=332(14)$ MeV

$oldsymbol{ ext{alpha}_s}(m_Z)=0.1179(12)$

Error from perturbative step estimated as 0.0002

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 $\alpha > 0.2$ and at the same time has the physical scales small compared to the cutoff $1/a$ in all stages of the computation. The result $\Lambda_\overline{MS}^{(3)}=332(14)$~MeV is translated to $\alpha_\overline{MS}(m_Z)=0.1179(10)(2)$ 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 $0.0002$.