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 ${\mathrm{\Lambda }}_{\overline{MS}}^{(3)}$. At the $Z$ boson mass scale, we obtain ${\alpha }_s^{(5)}(M_Z)=0.1181(3){(}_{-12}^{+14})$, where the first error is statistical and the second is our estimate of various systematic uncertainties.