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

We perform hybrid Monte Carlo simulation of (2+1+1)-flavors lattice QCD with the optimal domain-wall fermion (which has the effective 4D Dirac operator exactly equal to the Zolotarev optimal rational approximation of the overlap Dirac 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 the plaquette 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 masses of the vector mesons $\phi(1020)$ and $J/\psi(3097)$ respectively; while the mass of the $u/d$ quarks is heavier than their physical values, with the unitary pion mass $M_\pi \simeq 280$ MeV (and $M_\pi L \simeq 3$). We compute the point-to-point quark propagators, and measure the time-correlation functions of meson and baryon interpolators. Our results of the mass spectra of the lowest-lying hadrons containing $s$ and $c$ quarks are in good agreement with the high energy experimental values, together with the predictions of the charmed baryons which have not been observed in experiments.