Determination of the QCD coupling from the static energy and the free energy

Understand

We present two determinations of the strong coupling \(\alpha_s\).

• The first one is from the static energy at three-loop accuracy, and may be considered an update of earlier determinations by some of us.
• The new analysis includes new lattice data at smaller lattice spacings, and reaches distances as short as \(0.0237\,{\rm fm}\).
• We present a comprehensive and detailed estimate of the error sources that contribute to the uncertainty of the final result, $\alpha_s(M_Z)=0.11660^{+0.00110}_{-0.00056}$.