Strong coupling constant from vacuum polarization functions in three-flavor lattice QCD with dynamical overlap fermions

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 Lambda (3)/MS. At the Z boson mass scale, we obtain alpha((5))(s) (MZ) = 0.1181(3)((+14)(-12) ), where the first error is statistical and the second is our estimate of various systematic uncertainties.