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We determine the strong coupling constant $α_s$ 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 $Λ_overlineMS^(3)$. At the $Z$ boson mass scale, we obtain $α_s^(5)(M_Z)=0.1181(3)(^+14_-12)$, where the first error is statistical and the second is our estimate of various systematic uncertainties.
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