Abstract
We determine the strong coupling constant \$\alpha\_s\$ from a lattice
calculation of vacuum polarization functions (VPF) in three-flavor QCD with
dynamical overlap fermions. Fitting lattice data of VPF to the continuum
perturbative formula including the operator product expansion, we extract the
QCD scale parameter \$Łambda\_MS^(3)\$. At the \$Z\$ boson mass
scale, we obtain \$\alpha\_s^(5)(M\_Z)=0.1181(3)(^+14\_-12)\$, where the first
error is statistical and the second is our estimate of various systematic
uncertainties.
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