We determine $D$ and $D_s$ decay constants from lattice QCD with 2% errors, 4 times better than experiment and previous theory: $f_{D_s}=241(3)\mathrm{MeV}$, $f_D=207(4)\mathrm{MeV}$, and $f_{D_s}/f_D=1.164(11)$. We also obtain $f_K/f_{\pi }=1.189(7)$ and $(f_{D_s}/f_D)/(f_K/f_{\pi })=0.979(11)$. Combining with experiment gives $V_{\mathrm{us}}=0.2262(14)$ and $V_{\mathrm{cs}}/V_{\mathrm{cd}}$ of 4.43(41). We use a highly improved quark discretization on MILC gluon fields that include realistic sea quarks, fixing the $u/d$, $s$, and $c$ masses from the $\pi$, $K$, and ${\eta }_c$ meson masses. This allows a stringent test against experiment for $D$ and $D_s$ masses for the first time (to within 7 MeV).

• Received 14 June 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.062002