${\Lambda }_{\overline{\text{MS}}}^{(n_f=2)}$ from a momentum space analysis of the quark-antiquark static potential

Abstract

We determine ${\Lambda }_{\overline{\text{MS}}}^{(n_f=2)}$ by fitting perturbative expressions for the quark-antiquark static potential to lattice results for QCD with $n_f=2$ dynamical quark flavors. To this end we use the perturbative static potential at the presently best known accuracy, i.e. up to $\mathcal{O}({\alpha }_s^4)$, in momentum space. The lattice potential is computed on a fine lattice with $a\approx 0.042\text{fm}$ in position space. To allow for a comparison and matching of both results, the lattice potential is transformed into momentum space by means of a discrete Fourier transform. The value of ${\Lambda }_{\overline{\text{MS}}}^{(n_f=2)}$ is extracted in momentum space. All sources of statistical and systematic errors are discussed. The uncertainty in the value of ${\Lambda }_{\overline{\text{MS}}}^{(n_f=2)}$ is found to be smaller than that obtained in a recent position space analysis of the static potential based on the same lattice data.

Comments: 30 pages, 6 figures; some clarifications added, matches journal version