Precision determination of r_0Lambda_MS from the QCD static energy

TL;DR

This paper determines the QCD scale parameter r_0Lambda_MS by comparing high-precision theoretical static energy expressions with lattice data, providing a method to extract fundamental QCD parameters.

Contribution

It introduces a novel approach to accurately determine r_0Lambda_MS using next-to-next-to-next-to leading-logarithmic static energy calculations and lattice data comparison.

Findings

r_0Lambda_MS=0.637^{+0.032}_{-0.030} for zero flavors

Method applicable to unquenched lattice data for future scale determination

Provides a pathway to determine the lattice scale r_0 using alpha_s input

Abstract

We use the recently obtained theoretical expression for the complete QCD static energy at next-to-next-to-next-to leading-logarithmic accuracy to determine r_0Lambda_MS by comparison with available lattice data, where r_0 is the lattice scale and Lambda_MS is the QCD scale. We obtain r_0Lambda_MS=0.637^{+0.032}_{-0.030} for the zero-flavor case. The procedure we describe can be directly used to obtain r_0Lambda_MS in the unquenched case, when unquenched lattice data for the static energy at short distances becomes available. Using the value of the strong coupling alpha_s as an input, the unquenched result would provide a determination of the lattice scale r_0.