Measurements of branching fractions of leptonic and hadronic $D_s^{+}$ meson decays and extraction of the $D_s^{+}$ meson decay constant

We present measurements of absolute branching fractions of hadronic and lep-tonic $D_s^{+}$ decays to K ^- K ⁺ π ⁺, ${\overline{K}}^0$ K ⁺, ηπ ⁺, μ ⁺ ν _μ and τ ⁺ ν _τ and report a search for the leptonic $D_s^{+}$ → e ⁺ ν _e decays. The results are obtained from a data sample of 913 fb^-1 collected at or near the ${\rm Y}$(4S) and ${\rm Y}$(5S) resonances with the Belle detector at the KEKB asymmetric-energy e ⁺ e ^- collider. The branching fractions of hadronic decays are measured to be $B\left(D_s^{+}\to K^{-}{K}^{+}{\pi }^{+}\right)=\left(5.06\pm 0.15\pm 0.21\right)\%$, $B\left(D_s^{+}\to {\overline{K}}^0{K}^{+}\right)=\left(2.95\pm 0.11\pm 0.09\right)\%$, $B\left(D_s^{+}\to \eta {\pi }^{+}\right)=\left(1.82\pm 0.14\pm 0.07\right)\%$, where the first and second uncertainties are statistical and systematic, respectively. The branching fractions of leptonic decays are measured to be $B\left(D_s^{+}\to {\mu }^{+}{\nu }_{\mu }\right)=\left(0.531\pm 0.028\pm 0.020\right)\%$, $B\left(D_s^{+}\to {\tau }^{+}{\nu }_{\tau }\right)=\left(5.70\pm {0.21}_{-0.30}^{-0.31}\right)\%$, which are combined to determine the $D_s^{+}$ meson decay constant $f_{D_s}=\left(255.5\pm 4.2\pm 5.1\right)MeV$. We find no significant signal for $D_s^{+}\to e^{+}{\nu }_e$ decays and set an upper limit of $B\left(D_s^{+}\to e^{+}{\nu }_e\right)$ < 1.0(0.83) × 10^-4 at 95% (90%) confidence level.