Precision Measurement of the Branching Fraction of D+ →μ+νμ

Using 20.3 fb-1 of e+e- collision data collected at a center-of-mass energy of Ec.m.=3.773 GeV with the BESIII detector operating at the BEPCII collider, we determine the branching fraction of the leptonic decay D+→μ+νμ to be (4.034±0.080stat±0.040syst)×10-4. Interpreting our measurement with knowledge of the Fermi coupling constant GF, the masses of the D+ and μ+ as well as the lifetime of the D+, we determine fD+|Vcd|=(48.02±0.48stat±0.24syst±0.12input±0.15EM) 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 |Vcd| given by the global standard model fit, we obtain the D+ decay constant fD+=(213.5±2.1stat±1.1syst±0.8input±0.7EM) MeV. Alternatively, using the value of fD+ from a precise lattice quantum chromodynamics calculation, we extract |Vcd|=0.2265±0.0023stat±0.0011syst±0.0009input±0.0007EM.