Determination of alpha_s from the QCD static energy

TL;DR

This paper compares lattice QCD data with high-precision perturbative calculations of the static energy to determine the strong coupling constant alpha_s at low and high energies, achieving three-loop accuracy and resummation of ultrasoft logs.

Contribution

It provides a novel determination of alpha_s at low energy from lattice data using advanced perturbative techniques up to N^3LL accuracy.

Findings

Alpha_s(1.5 GeV)=0.326±0.019

Alpha_s(M_Z)=0.1156^{+0.0021}_{-0.0022}

Perturbation theory describes lattice data well at short distances.

Abstract

We compare lattice data for the short-distance part of the static energy in 2+1 flavor quantum chromodynamics (QCD) with perturbative calculations, up to next-to-next-to-next-to leading-logarithmic accuracy. We show that perturbation theory describes very well the lattice data at short distances, and exploit this fact to obtain a determination of the product of the lattice scale r_0 with the QCD scale Lambda_{MS}. With the input of the value of r_0, this provides a determination of the strong coupling alpha_s at the typical distance scale of the lattice data. We obtain alpha_s(1.5 GeV)=0.326\pm0.019, which provides a novel determination of alpha_s at low energy and with three-loop accuracy (including resummation of the leading ultrasoft logarithms). When this value is evolved to the Z-mass scale M_Z, it corresponds to alpha_s(M_Z)=0.1156^{+0.0021}_{-0.0022}.