A low-energy determination of $\alpha_s$ at three loops

TL;DR

This paper presents a precise low-energy determination of the strong coupling constant _s by comparing three-loop QCD static energy calculations with lattice QCD data, resulting in an accurate value at the Z boson mass scale.

Contribution

The paper provides a novel, high-precision extraction of _s at low energy using three-loop calculations and lattice QCD comparison, improving the accuracy of _s measurements.

Findings

_s(1.5 GeV) = 0.336^{+0.012}_{-0.008}

_s(M_Z) = 0.1166^{+0.0012}_{-0.0008}

Demonstrates the effectiveness of three-loop calculations in low-energy _s determination.

Abstract

We review one of the most accurate low-energy determinations of $\alpha_s$. Comparing at short distances the QCD static energy at three loops and resummation of the next-to-next-to leading logarithms with its determination in 2+1-flavor lattice QCD, we obtain $\alpha_s(1.5~{\rm GeV})=0.336^{+0.012}_{-0.008}$, which corresponds to $\alpha_s(M_Z)=0.1166^{+0.0012}_{-0.0008}$. We discuss future perspectives.