Decay Constants of Pseudoscalar $D$-mesons in Lattice QCD with Domain-Wall Fermion

We present the first study of the masses and decay constants of the pseudoscalar $D$ mesons in two flavors lattice QCD with domain-wall fermion. The gauge ensembles are generated on the ${24}^3\times 48$ lattice with the extent $N_s=16$ in the fifth dimension, and the plaquette gauge action at $\beta =6.10$, for three sea-quark masses with corresponding pion masses in the range $260-475$ MeV. We compute the point-to-point quark propagators, and measure the time-correlation functions of the pseudoscalar and vector mesons. The inverse lattice spacing is determined by the Wilson flow, while the strange and the charm quark masses by the masses of the vector mesons $\varphi (1020)$ and $J\mathrm{/}\psi (3097)$ respectively. Using heavy meson chiral perturbation theory (HMChPT) to extrapolate to the physical pion mass, we obtain $ f_D = 202.3(2.2)(2.6) $MeVand$ f_{D_s} = 258.7(1.1)(2.9) $ MeV.