Strong coupling constant and quark masses from lattice QCD

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 (HMrASχPT) can help in these determinations. After critically reviewing different lattice results we determine lattice world averages for the strong coupling constant, αs(MZ,Nf=5)=0.11803−0.00068+0.00047, as well as for the charm-quark mass, mc(mc,Nf=4)=1.2735(35) GeV, and the bottom-quark mass, mb(mb,Nf=5)=4.188(10) GeV. The above determinations are more precise than the ones obtained by Particle Data Group (PDG).