Precision Measurement of the Branching Fraction of D^{+}→μ^{+}ν_{μ}

Using 20.3  fb^{-1} of e^{+}e^{-} collision data collected at a center-of-mass energy of E_{c.m.}=3.773  GeV with the BESIII detector operating at the BEPCII collider, we determine the branching fraction of the leptonic decay D^{+}→μ^{+}ν_{μ} to be (4.034±0.080_{stat}±0.040_{syst})×10^{-4}. Interpreting our measurement with knowledge of the Fermi coupling constant G_{F}, the masses of the D^{+} and μ^{+} as well as the lifetime of the D^{+}, we determine f_{D^{+}}|V_{cd}|=(48.02±0.48_{stat}±0.24_{syst}±0.12_{input}±0.15_{EM})  MeV after taking into account necessary radiative corrections. This result is a factor of 2.3 more precise than the previous best measurement. Using the value of the magnitude of the c→d Cabibbo-Kobayashi-Maskawa matrix element |V_{cd}| given by the global standard model fit, we obtain the D^{+} decay constant f_{D^{+}}=(213.5±2.1_{stat}±1.1_{syst}±0.8_{input}±0.7_{EM})  MeV. Alternatively, using the value of f_{D^{+}} from a precise lattice quantum chromodynamics calculation, we extract |V_{cd}|=0.2265±0.0023_{stat}±0.0011_{syst}±0.0009_{input}±0.0007_{EM}.