Scale Setting The Mobius Domain Wall Fermion On Gradient-Flowed Hisq Action Using The Omega Baryon Mass And The Gradient-Flow Scales T(0) And W(0)

We report on a subpercent scale determination using the omega baryon mass and gradient-flow methods. The calculations are performed on 22 ensembles of N-f = 2 1 1 highly improved, rooted staggered sea-quark configurations generated by the MILC and CalLat Collaborations. The valence quark action used is Mobius domain wall fermions solved on these configurations after a gradient-flow smearing is applied with a flowtime of t(gf) = 1 in lattice units. The ensembles span four lattice spacings in the range 0.06 less than or similar to a less than or similar to 0.15 fm, six pion masses in the range 130 less than or similar to m(pi) less than or similar to 400 MeV and multiple lattice volumes. On each ensemble, the gradient-flow scales t(0)/a(2) and w(0)/a and the omega baryon mass am(Omega) are computed. The dimensionless product of these quantities is then extrapolated to the continuum and infinite volume limits and interpolated to the physical light, strange and charm quark mass point in the isospin limit, resulting in the determination of root t(0) = 0.1422(14) fm and w(0) = 0.1709(11) fm with all sources of statistical and systematic uncertainty accounted for. The dominant uncertainty in both results is the stochastic uncertainty, though for root t(0 )there are comparable continuum extrapolation uncertainties. For w(0), there is a clear path for a few-per-mille uncertainty just through improved stochastic precision, as recently obtained by the Budapest-Marseille-Wuppertal Collaboration.