We present lattice determinations of the heavy quark masses and the strong coupling constant obtained by two different methods in (2+1)-flavor QCD with Highly Improved Staggered Quark (HISQ) action.
Using lattice calculations of the moments of the pseudoscalar quarkonium correlators at several values of the heavy valence quark mass we determine the strong coupling constant in $\overline{MS}$ scheme at four low energy scales corresponding to $m_c$, $1.5m_c$, $2m_c$ and $3m_c$, with $m_c$ being the charm quark mass. We obtain $\Lambda_{\overline{MS}}^{n_f=3}=298 \pm 16$ MeV, which
is equivalent to $\alpha_s(\mu=M_Z,n_f=5)=0.1159(12)$. For the charm and bottom quark masses in $\overline{MS}$ scheme we obtain: $m_c(\mu=m_c,n_f=4)=1.265(10)$ GeV and $m_b(\mu=m_b,n_f=5)=4.188(37)$ GeV.
Using lattice calculations of the QCD static energy at $T=0$, or the static singlet free energy at $T>0$ we obtain $\alpha_s(M_Z)=0.11660^{+0.00110}_{-0.00056}$, or $\alpha_s(M_Z)=0.11638^{+0.0009 5}_{-0.00087}$. The novel feature of our analyses that many lattice spacings are used in the continuum extrapolations, with the smallest lattice spacings at $T=0$, or at $T>0$ being $a=0.025$ fm, or $a=0.008$ fm, respectively.