QCD Coupling from a Nonperturbative Determination of the Three-Flavor Λ Parameter

We present a lattice determination of the Λ parameter in three-flavor QCD and the strong coupling at the Z pole mass. Computing the nonperturbative running of the coupling in the range from 0. 2 to 70 GeV, and using experimental input values for the masses and decay constants of the pion and the kaon, we obtain Λ₌ₒ₎ₕ₄ₑ ¯^ (3) =341 (12) MeV. The nonperturbative running up to very high energies guarantees that systematic effects associated with perturbation theory are well under control. Using the four-loop prediction for Λ₌ₒ₎ₕ₄ₑ ¯^ (5) /Λ₌ₒ₎ₕ₄ₑ ¯^ (3) yields α₌ₒ₎ₕ₄ₑ ¯^ (5) (mₙ) =0. 11852 (84).