${\alpha }_s$ from the Lattice Hadronic Vacuum Polarisation

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 ${\alpha }_s(M_Z)=0.1181(27{)}_{-22}^{+8}$, where the first error is statistical and the second systematic.

Cited by in corpus (5)

• Snowmass 2021 whitepaper: Proton structure at the precision frontier
• Hadronic vacuum polarization contribution to the muon $g-2$ with 2+1 flavor lattice QCD on a larger than (10 fm${)}^4$ lattice at the physical point
• Strong coupling constant and heavy quark masses in 2+1 flavor QCD
• Running coupling constant from position-space current-current correlation functions in three-flavor lattice QCD
• Lattice determinations of the strong coupling