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

Abstract 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 $ \varUpsilon $ (4S) and $ \varUpsilon $ (5S) resonances with the Belle detector at the KEKB asymmetric-energy e + e − collider. The branching fractions of hadronic decays are measured to be $ \begin{array}{*{20}{c}} {\mathcal{B}\left( {D_s^{+}\ \to\ {K^{-}}{K^{+}}{\pi^{+}}} \right) = \left( {5.06\pm 0.15\pm 0.21} \right)\%,} \\ {\mathcal{B}\left( {D_s^{+}\ \to\ {{\overline{K}}^0}{K^{+}}} \right) = \left( {2.95\pm 0.11\pm 0.09} \right)\%,} \\ {\mathcal{B}\left( {D_s^{+}\ \to\ \eta {\pi^{+}}} \right) = \left( {1.82\pm 0.14\pm 0.07} \right)\%,} \\ \end{array} $ where the first and second uncertainties are statistical and systematic, respectively. The branching fractions of leptonic decays are measured to be $ \begin{array}{*{20}{c}} {\mathcal{B}\left( {D_s^{+}\ \to\ {\mu^{+}}{\nu_{\mu }}} \right)=\left( {0.531\pm 0.028\pm 0.020} \right)\%,} \\ {\mathcal{B}\left( {D_s^{+}\to {\tau^{+}}{\nu_{\tau }}} \right)=\left( {5.70\pm 0.21_{-0.30}^{-0.31 }} \right)\%,} \\ \end{array} $ which are combined to determine the $ D_s^{+} $ meson decay constant $ {f_{{{D_s}}}}=\left( {255.5\pm 4.2\pm 5.1} \right)\ \mathrm{MeV}. $ We find no significant signal for $ D_s^{+} $ → e + ν e decays and set an upper limit of $ \mathcal{B}\left( {D_s^{+}\ \to\ {e^{+}}{\nu_e}} \right) $ < 1.0(0.83) × 10−4 at 95% (90%) confidence level.