Determining the QCD coupling from lattice vacuum polarization

TL;DR

This paper presents a lattice QCD method to determine the strong coupling constant by analyzing vacuum polarization, effectively managing lattice artifacts and offering a competitive alternative to sum rule analyses.

Contribution

It introduces a lattice calculation of vacuum polarization across multiple momentum directions to accurately extract the QCD coupling, addressing non-perturbative and discretization effects.

Findings

Results are competitive with sum rule analyses.

Many momentum directions help monitor lattice artifacts.

Systematic advantages over phenomenological methods.

Abstract

The QCD coupling appears in the perturbative expansion of the current-current two-point (vacuum polarization) function. Any lattice calculation of vacuum polarization is plagued by several competing non-perturbative effects at small momenta and by discretization errors at large momenta. We work in an intermediate region, computing the vacuum polarization for many off-axis momentum directions on the lattice. Having many momentum directions provides a way to monitor and account for lattice artifacts. Our results are competitive with, and have certain systematic advantages over, the alternate phenomenological determination of the strong coupling from the same light quark vacuum polarization produced by sum rule analyses of hadronic tau decay data.