Strong coupling in (2+1+1)-flavor QCD

Abstract

The strong coupling $\alpha_\mathrm{s}$ can be obtained from the static energy as shown in previous lattices studies. For short distances, the static energy can be calculated both on the lattice with the use of Wilson line correlators, and with the perturbation theory up to three loop accuracy with leading ultrasoft log resummation. Comparing the perturbative expression and lattice data allows for precise determination of $\alpha_\mathrm{s}(m_Z)$. We will present preliminary results for the determination of $\alpha_\mathrm{s} {(M_Z)}$ in (2+1+1)-flavor QCD using the configurations made availableby the MILC-collaboration with smallest lattice spacing reaching 0.0321fm.