Measurement of the Pseudoscalar Decay Constant $f_{D_s}$ Using Charm-Tagged Events in $e^{+}{e}^{-}$ Collisions at $\sqrt{s}=10.58\mathrm{GeV}$

Using $230.2{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ annihilation data collected with the BABAR detector at and near the peak of the ${\rm Y}(4S)$ resonance, $489\pm 55$ events containing the pure leptonic decay $D_s^{+}\to {\mu }^{+}{\nu }_{\mu }$ have been isolated in charm-tagged events. The ratio of partial widths $\Gamma (D_s^{+}\to {\mu }^{+}{\nu }_{\mu })/\Gamma (D_s^{+}\to \varphi {\pi }^{+})$ is measured to be $0.143\pm 0.018\pm 0.006$ allowing a determination of the pseudoscalar decay constant $f_{D_s}=(283\pm 17\pm 7\pm 14)\mathrm{MeV}$. The errors are statistical, systematic, and from the $D_s^{+}\to \varphi {\pi }^{+}$ branching ratio, respectively.