Determination of $\Lambda_{\overline{\textrm{MS}}}^{(n_f=2)}$ and analytic parameterization of the static quark-antiquark potential

TL;DR

This paper determines the QCD scale parameter $\Lambda_{ar{ ext{MS}}}$ for two flavors by matching perturbative and lattice results of the static quark-antiquark potential, and provides an analytic potential useful for phenomenology.

Contribution

It introduces a method to extract $\Lambda_{ar{ ext{MS}}}$ for $n_f=2$ by matching lattice and perturbative potentials and offers a comprehensive analytic parameterization of the static potential.

Findings

Successfully extracted $\Lambda_{ar{ ext{MS}}}$ for $n_f=2$.

Provided an analytic form of the static quark-antiquark potential.

Applied the potential to compute the bottomonium spectrum.

Abstract

While lattice QCD allows for reliable results at small momentum transfers (large quark separations), perturbative QCD is restricted to large momentum transfers (small quark separations). The latter is determined up to a reference momentum scale $\Lambda$, which is to be provided from outside, e.g. from experiment or lattice QCD simulations. In this article, we extract $\Lambda_{\overline{\textrm{MS}}}$ for QCD with $n_f=2$ dynamical quark flavors by matching the perturbative static quark-antiquark potential in momentum space to lattice results in the intermediate momentum regime, where both approaches are expected to be applicable. In a second step, we combine the lattice and the perturbative results to provide a complete analytic parameterization of the static quark-antiquark potential in position space up to the string breaking scale. As an exemplary phenomenological application of our all-distances potential we compute the bottomonium spectrum in the static limit.