High-precision scale setting with the Ω -baryon mass and gradient flow

The gradient-flow scale w 0 in lattice QCD is determined using the mass of the Ω − baryon to set the physical scale. Nine ensembles using the highly improved staggered quark (HISQ) action with lattice spacings of 0.15 fm down to 0.04 fm are used, seven of which have nearly physical light-quark masses. Electromagnetic corrections to the Ω − mass are defined in order to compute a pure-QCD Ω mass. The final result is w 0 = 0.17187 ( 68 ) fm , corresponding to a relative uncertainty of 0.40% and a central value in good agreement with previous calculations in the literature.