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We calculate the up-, down-, strange-, charm-, and bottom-quark masses usingthe MILC highly improved staggered-quark ensembles with four flavors ofdynamical quarks. We use ensembles at six lattice spacings ranging from$a\approx0.15$~fm to $0.03$~fm and with both physical and unphysical values ofthe two light and the strange sea-quark masses. We use a new method based onheavy-quark effective theory (HQET) to extract quark masses from heavy-lightpseudoscalar meson masses. Combining our analysis with our separatedetermination of ratios of light-quark masses we present masses of the up,down, strange, charm, and bottom quarks. Our results for the$\overline{\text{MS}}$-renormalized masses are $m_u(2~\text{GeV}) =2.130(41)$~MeV, $m_d(2~\text{GeV}) = 4.675(56)$~MeV, $m_s(2~\text{GeV}) =92.47(69)$~MeV, $m_c(3~\text{GeV}) = 983.7(5.6)$~MeV, and $m_c(m_c) =1273(10)$~MeV, with four active flavors; and $m_b(m_b) = 4195(14)$~MeV withfive 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 theother masses and all quoted ratios are the most precise to date. Moreover,these results are the first with a perturbative accuracy of $\alpha_s^4$. Asbyproducts of our method, we obtain the matrix elements of HQET operators withdimension 4 and 5: $\overline{\Lambda}_\text{MRS}=555(31)$~MeV in the minimalrenormalon-subtracted (MRS) scheme, $\mu_\pi^2 = 0.05(22)~\text{GeV}^2$, and$\mu_G^2(m_b)=0.38(2)~\text{GeV}^2$. The MRS scheme [Phys. Rev. D97, 034503(2018), arXiv:1712.04983 [hep-ph]] is the key new aspect of our method.

Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD