Abstract
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 M\"obius domain wall fermions solved on these configurations after a gradient-flow smearing is applied with a flowtime of ${t}_{\mathrm{gf}}=1$ in lattice units. The ensembles span four lattice spacings in the range $0.06\ensuremath{\lesssim}a\ensuremath{\lesssim}0.15\text{ }\text{ }\mathrm{fm}$, six pion masses in the range $130\ensuremath{\lesssim}{m}_{\ensuremath{\pi}}\ensuremath{\lesssim}400\text{ }\text{ }\mathrm{MeV}$ and multiple lattice volumes. On each ensemble, the gradient-flow scales ${t}_{0}/{a}^{2}$ and ${w}_{0}/a$ and the omega baryon mass $a{m}_{\mathrm{\ensuremath{\Omega}}}$ 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 $\sqrt{{t}_{0}}=0.1422(14)\text{ }\text{ }\mathrm{fm}$ and ${w}_{0}=0.1709(11)\text{ }\text{ }\mathrm{fm}$ with all sources of statistical and systematic uncertainty accounted for. The dominant uncertainty in both results is the stochastic uncertainty, though for $\sqrt{{t}_{0}}$ 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.
Highlights
Lattice QCD (LQCD) has become a prominent theoretical tool for calculations of hadronic quantities, and many calculations have reached a level of precision to be able to supplement and/or complement experimental determinations [1]
In this paper we present a precision scale setting for our mixed lattice action [15] which uses Nf 1⁄4 2 þ 1 þ 1 highly improved, rooted staggered sea-quark (HISQ) configurations generated by the MILC [16] and CalLat Collaborations and Möbius domain wall fermions for the pvaffilffieffi nce sector
On all but one of the 22 ensembles, the strange quark mass is close to its physical value, allowing us to perform a simple interpolation to the physical strange quark mass point
Summary
Lattice QCD (LQCD) has become a prominent theoretical tool for calculations of hadronic quantities, and many calculations have reached a level of precision to be able to supplement and/or complement experimental determinations [1]. There are many quantities for which a precise scale setting is desirable, such as the hadron spectrum, the nucleon axial radius, the hadronic contribution to the muon g − 2 [2] and many others In these cases, a quantity which is dimensionful (after multiplying or dividing by an appropriate power of the lattice spacing) is calculated and compared to experiment, following extrapolations to the physical point in lattice spacing, volume, and pion mass. The gradient flow scales t0 [4] and w0 [5] have been used for a more precise determination of the lattice spacing [6,7,8,9,10,11,12,13,14] In this case, a well-controlled extrapolation of these quantities to the physical point is necessary.
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