Pseudoscalar Decay Constants $f_D$ and $f_{D_s}$ in Lattice QCD with Exact Chiral Symmetry

We determine the masses and decay constants of pseudoscalar mesons $D$, $D_s$, and $K$ in quenched lattice QCD with exact chiral symmetry. For 100 gauge configurations generated with single-plaquette action at $\beta =6.1$ on the ${20}^3\times 40$ lattice, we compute point-to-point quark propagators for 30 quark masses in the range $0.03\le m_{q}a\le 0.80$, and measure the time-correlation functions of pseudoscalar and vector mesons. The inverse lattice spacing $a^{-1}$ is determined with the experimental input of $f_{\pi }$, while the strange quark bare mass $m_{s}a=0.08$, and the charm quark bare mass $m_{c}a=0.80$ are fixed such that the masses of the corresponding vector mesons are in good agreement with $\varphi (1020)$ and $J\mathrm{/}\psi (3097)$ respectively. Our results of pseudoscalar-meson decay constants are $ f_K = 152(6)(10) $MeV,$ f_D = 235(8)(14)$MeV,and$ f_{D_s} = 266(10)(18) $ MeV.