$\hat{I}{\pm }_s$ from the Lattice Hadronic Vacuum Polarisation

Abstract

We present a determination of the QCD coupling constant, $\hat{I}{\pm }_s$, 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 $\hat{I}{\pm }_s(M_Z)=0.1181(27{)}_{-22}^{+8}$, where the first error is statistical and the second systematic.