We calculate the up-, down-, strange-, charm-, and bottom-quark masses using the MILC highly improved staggered-quark ensembles with four flavors of dynamical quarks. We use ensembles at six lattice spacings ranging from a ≈ 0.15 to 0.03?fm and with both physical and unphysical values of the two light and the strange sea-quark masses. We use a new method based on heavy-quark effective theory (HQET) to extract quark masses from heavy-light pseudoscalar meson masses. Combining our analysis with our separate determination of ratios of light-quark masses we present masses of the up, down, strange, charm, and bottom quarks. Our results for the MS ˉ -renormalized masses are m u ( 2 ? ? GeV ) = 2.130 ( 41 ) ? ? MeV , m d ( 2 ? ? GeV ) = 4.675 ( 56 ) ? ? MeV , m s ( 2 ? ? GeV ) = 92.47 ( 69 ) ? ? MeV , m c ( 3 ? ? GeV ) = 983.7 ( 5.6 ) ? ? MeV , and m c ( m c ) = 1273 ( 10 ) ? ? MeV , with four active flavors; and m b ( m b ) = 4195 ( 14 ) ? ? MeV with five active flavors. We also obtain ratios of quark masses m c / m s = 11.783 ( 25 ) , m b / m s = 53.94 ( 12 ) , and m b / m c = 4.578 ( 8 ) . The result for m c matches the precision of the most precise calculation to date, and the other masses and all quoted ratios are the most precise to date. Moreover, these results are the first with a perturbative accuracy of α s 4 . As byproducts of our method, we obtain the matrix elements of HQET operators with dimension 4 and 5: Λ ˉ MRS = 555 ( 31 ) ? ? MeV in the minimal renormalon-subtracted (MRS) scheme, μ π 2 = 0.05 ( 22 ) ? ? GeV 2 , and μ G 2 ( m b ) = 0.38 ( 2 ) ? ? GeV 2 . The MRS scheme [Phys. Rev. D 97 , 034503 (2018)] is the key new aspect of our method.
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机译：我们使用高度改进的MILC交错夸克合奏以及四种动态夸克来计算上，下，奇异，魅力和底部夸克的质量。我们使用从≈0.15到0.03？fm的六个晶格间距的合奏，并具有两个轻质和奇异海夸克质量的物理值和非物理值。我们使用基于重夸克有效理论（HQET）的新方法从重轻伪标量介子质量中提取夸克质量。将我们的分析与对轻夸克质量比率的单独确定相结合，我们将呈现上夸克，下夸克，奇异夸克，魅力夸克和底部夸克的质量。我们对MSˉ重归一化质量的结果是m u（2？？GeV）= 2.130（41）？ ？ MeV，m d（2≤GeV）＝ 4.675（56）≤m。 ？ MeV，ms（2≤GeV）＝ 92.47（69）≤m。 ？ MeV，m c（3≤GeV）＝ 983.7（5.6）≤m。 ？ MeV和m c（m c）= 1273（10）？ ？ MeV，具有四种活性风味;而m b（m b）= 4195（14）？ ？具有五种活性风味的MeV。我们还获得了夸克质量比m c / m s = 11.783（25），m b / m s = 53.94（12）和m b / m c = 4.578（8）。 m c的结果与迄今为止最精确的计算的精度匹配，其他质量和所有引用的比率都是迄今为止最精确的计算。此外，这些结果是第一个具有αs 4摄动精度的结果。作为我们方法的副产品，我们获得了尺寸为4和5的HQET算子的矩阵元素：ΛˉMRS = 555（31）？ ？ MeV在最小减法线数（MRS）方案中，μπ2 = 0.05（22）？ ？ GeV 2和μG 2（m b）= 0.38（2）？ ？ GeV 2。 MRS方案[Phys。 Rev B 97、034503（2018）]是我们方法的关键新方面。
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