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In our analysis published in our paper, we found an error in the code to convert the strong coupling constant obtained by lattice QCD on Nf 1⁄4 2þ 1 at 2 GeV to that in Nf 1⁄4 5 at the MZ scale using the next-to-leading order in the MS scheme [1]. The central value as well as the systematic error is modified from Table I in our paper to Table I. The final value of αð5Þ s ðMZÞ in the Abstract and Eq. (17) in our paper should be changed to αð5Þ s ðMZÞ 1⁄4 0.1118ð3Þ þ16 −17 : (1)

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Erratum: Strong coupling constant from vacuum polarization functions in three-flavor lattice QCD with dynamical overlap fermions [Phys. Rev. D 82, 074505 (2010)]