$\Lambda_{\bar{\textrm{MS}}}^{(n_f=2)}$ from a momentum space analysis of the quark-antiquark static potential

TL;DR

This paper accurately determines the QCD scale parameter $\\Lambda_{\bar{MS}}^{(n_f=2)}$ by fitting high-precision lattice QCD static potential data in momentum space to perturbative calculations, reducing uncertainties compared to previous position space methods.

Contribution

It introduces a momentum space analysis of the static potential for extracting $\Lambda_{\bar{MS}}^{(n_f=2)}$, achieving smaller uncertainties than prior position space approaches.

Findings

Precise value of $\Lambda_{\bar{MS}}^{(n_f=2)}$ with reduced uncertainty.

Demonstration of effective momentum space analysis for lattice QCD data.

Comparison showing improved accuracy over previous position space analyses.

Abstract

We determine $\Lambda_{\bar{\textrm{MS}}}^{(n_f=2)}$ 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 ${\cal O}(\alpha_s^4)$, in momentum space. The lattice potential is computed on a fine lattice with $a \approx 0.042 \, \textrm{fm}$ 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 $\Lambda_{\bar{\textrm{MS}}}^{(n_f=2)}$ is extracted in momentum space. All sources of statistical and systematic errors are discussed. The uncertainty in the value of $\Lambda_{\bar{\textrm{MS}}}^{(n_f=2)}$ is found to be smaller than that obtained in a recent position space analysis of the static potential based on the same lattice data.