Charmed-Meson Decay Constants in Three-Flavor Lattice QCD

We present the first lattice QCD calculation with realistic sea quark content of the $D^{+}$-meson decay constant $f_{D^{+}}$. We use the MILC Collaboration’s publicly available ensembles of lattice gauge fields, which have a quark sea with two flavors (up and down) much lighter than a third (strange). We obtain $f_{D^{+}}=201\pm 3\pm 17\mathrm{MeV}$, where the errors are statistical and a combination of systematic errors. We also obtain $f_{D_s}=249\pm 3\pm 16\mathrm{MeV}$ for the $D_s$ meson.

Figure 1

Chiral extrapolation of $R_{q/s}$ at $a=0.121\mathrm{fm}$. Data points show only statistical errors, but the systematic error of fitting is shown at left.

Figure 2

Dependence of ${\varphi }_s$ on $a^2$. Circles result from removing the $O(a^2)$ pieces in Eq. (10); squares omit this step.