Measurement ofB(Ds+→l+ν)and the decay constantfDS+

We examine $e^{+}{e}^{-}\to D_s^{-}{D}_s^{*+}$ and $D_s^{*-}{D}_s^{+}$ interactions at 4170 MeV using the CLEO-c detector in order to measure the decay constant $f_{D_s^{+}}$. We use the $D_s^{+}\to {\ell }^{+}\nu$ channel, where the ${\ell }^{+}$ designates either a ${\mu }^{+}$ or a ${\tau }^{+}$, when the ${\tau }^{+}\to {\pi }^{+}\overline{\nu }$. Analyzing both modes independently, we determine $\mathcal{B}(D_s^{+}\to {\mu }^{+}\nu )=(0.594\pm 0.066\pm 0.031)\%$, and $\mathcal{B}(D_s^{+}\to {\tau }^{+}\nu )=(8.0\pm 1.3\pm 0.4)\%$. We also analyze them simultaneously to find an effective value of ${\mathcal{B}}^{\mathrm{eff}}(D_s^{+}\to {\mu }^{+}\nu )=(0.638\pm 0.059\pm 0.033)\%$ and extract $f_{D_s^{+}}=274\pm 13\pm 7\mathrm{MeV}$. Combining with our previous determination of $\mathcal{B}(D^{+}\to {\mu }^{+}\nu )$, we also find the ratio $f_{D_s^{+}}/f_{D^{+}}=1.23\pm 0.11\pm 0.04$. We compare to current theoretical estimates. Finally, we find $\mathcal{B}(D_s^{+}\to e^{+}\nu )<1.3\times {10}^{-4}$ at 90% confidence level.