$\alpha_s$ from the Lattice Hadronic Vacuum Polarisation

TL;DR

This paper determines the strong coupling constant $oldsymbol{_s}$ using lattice QCD results for the hadronic vacuum polarization, fitting to continuum theory, and carefully managing systematic errors to achieve a precise $oldsymbol{_s(M_Z)}$ value.

Contribution

It provides a novel lattice QCD determination of $oldsymbol{_s}$ with controlled systematic uncertainties, improving the precision of the coupling constant measurement.

Findings

_s(M_Z)=0.1181(27)^{+8}_{-22}

Systematic errors were identified and addressed

Consistent results across multiple lattice spacings

Abstract

We present a determination of the QCD coupling constant, $\alpha_s$, obtained by fitting lattice results for the flavour $ud$ hadronic vacuum polarisation function to continuum perturbation theory. We use $n_f=2+1$ flavours of Domain Wall fermions generated by the RBC/UKQCD collaboration and three lattice spacings $a^{-1}=1.79,\, 2.38$ and $3.15\ \text{GeV}$. Several sources of potential systematic error are identified and dealt with. After fitting and removing expected leading cut-off effects, we find for the five-flavour $\overline{\text{MS}}$ coupling the value $\alpha_s(M_Z)=0.1181(27)^{+8}_{-22}$, where the first error is statistical and the second systematic.