Determination of the Pseudoscalar Decay Constant f_{D_{s}^{+}} via D_{s}^{+}→μ^{+}ν_{μ}

Abstract

Using a 3.19 fb^{-1} data sample collected at an e^{+}e^{-} center-of-mass energy of E_{cm}=4.178 GeV with the BESIII detector, we measure the branching fraction of the leptonic decay D_{s}^{+}→μ^{+}ν_{μ} to be B_{D_{s}^{+}→μ^{+}ν_{μ}}=(5.49±0.16_{stat}±0.15_{syst})×10^{-3}. Combining our branching fraction with the masses of the D_{s}^{+} and μ^{+} and the lifetime of the D_{s}^{+}, we determine f_{D_{s}^{+}}|V_{cs}|=246.2±3.6_{stat}±3.5_{syst} MeV. Using the c→s quark mixing matrix element |V_{cs}| determined from a global standard model fit, we evaluate the D_{s}^{+} decay constant f_{D_{s}^{+}}=252.9±3.7_{stat}±3.6_{syst} MeV. Alternatively, using the value of f_{D_{s}^{+}} calculated by lattice quantum chromodynamics, we find |V_{cs}|=0.985±0.014_{stat}±0.014_{syst}. These values of B_{D_{s}^{+}→μ^{+}ν_{μ}}, f_{D_{s}^{+}}|V_{cs}|, f_{D_{s}^{+}} and |V_{cs}| are each the most precise results to date.