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We perform hybrid Monte Carlo simulation of (2+1+1)-flavors lattice QCD withthe optimal domain-wall fermion (which has the effective 4D Dirac operatorexactly equal to the Zolotarev optimal rational approximation of the overlapDirac operator). The gauge ensemble is generated on the $32^3 \times 64 $lattice with the extent $ N_s = 16 $ in the fifth dimension, and with theplaquette gauge action at $ \beta = 6/g^2 = 6.20 $. The lattice spacing ($ a\simeq 0.063 $ fm) is determined by the Wilson flow, using the value $\sqrt{t_0} = 0.1416(8) $ fm obtained by the MILC Collaboration for the$(2+1+1)$-flavors QCD. The masses of $s$ and $c$ quarks are fixed by the massesof the vector mesons $ \phi(1020) $ and $ J/\psi(3097) $ respectively; whilethe mass of the $u/d$ quarks is heavier than their physical values, with theunitary pion mass $ M_\pi \simeq 280$ MeV (and $ M_\pi L \simeq 3 $). Wecompute the point-to-point quark propagators, and measure the time-correlationfunctions of meson and baryon interpolators. Our results of the mass spectra ofthe lowest-lying hadrons containing $ s $ and $ c $ quarks are in goodagreement with the high energy experimental values, together with thepredictions of the charmed baryons which have not been observed in experiments.

Lattice QCD with $N_f = 2+1+1 $ domain-wall quarks