We review lattice determinations of the charm and bottom quark masses and the strong coupling constant obtained by different methods. We explain how effective field theory approaches, such as Non-Relativistic QCD (NRQCD), potential Non-Relativistic QCD (pNRQCD), Heavy Quark Effective Theory (HQET) and Heavy Meson rooted All-Staggered Chiral Perturbation Theory (HMrAS$\chi$PT) can help in these determinations. After critically reviewing different lattice results we determine lattice world averages for the strong coupling constant, $\alpha_s(M_Z,N_f{=}5)=0.11803^{+0.00047}_{-0.00068}$, as well as for the charm quark mass, $m_c(m_c,N_f{=}4)=1.2735(35)$ GeV, and the bottom quark mass, $m_b(m_b,N_f{=}5)=4.188(10)$ GeV. The above determinations are more precise than the ones obtained by Particle Data Group (PDG).

中文翻译：

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来自晶格 QCD 的强耦合常数和夸克质量

我们回顾了魅力和底夸克质量的晶格测定以及通过不同方法获得的强耦合常数。我们解释了有效的场论方法，例如非相对论 QCD (NRQCD)、潜在非相对论 QCD (pNRQCD)、重夸克有效理论 (HQET) 和重介子根全交错手性扰动理论 (HMrAS$\chi$) PT) 可以帮助进行这些确定。在严格审查不同的晶格结果后，我们确定了强耦合常数 $\alpha_s(M_Z,N_f{=}5)=0.11803^{+0.00047}_{-0.00068}$ 以及粲夸克的晶格世界平均值质量 $m_c(m_c,N_f{=}4)=1.2735(35)$ GeV，底夸克质量 $m_b(m_b,N_f{=}5)=4.188(10)$ GeV。上述测定比 Particle Data Group (PDG) 获得的测定更精确。