Precision Measurement of the Branching Fraction of $D^{+}\to {\mu }^{+}{\nu }_{\mu }$

Using $20.3{\mathrm{f}\mathrm{b}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected at a center-of-mass energy of $E_{\mathrm{c}\mathrm{.}\mathrm{m}\mathrm{.}}=3.773$ GeV with the BESIII detector operating at the BEPCII collider, we determine the branching fraction of the leptonic decay $D^{+}\to {\mu }^{+}{\nu }_{\mu }$ to be $(4.034\pm {0.080}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.040}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}})\times {10}^{-4}$. Interpreting our measurement with knowledge of the Fermi coupling constant $G_F$, the masses of the $D^{+}$ and ${\mu }^{+}$ as well as the lifetime of the $D^{+}$, we determine $f_{D^{+}}\mathrm{\mid }{V}_{cd}\mathrm{\mid }=(48.02\pm {0.48}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.24}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}\pm {0.12}_{\mathrm{i}\mathrm{n}\mathrm{p}\mathrm{u}\mathrm{t}}\pm {0.15}_{\mathrm{E}\mathrm{M}})\mathrm{M}\mathrm{e}\mathrm{V}$ 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 $c\to d$ Cabibbo-Kobayashi-Maskawa matrix element $\mathrm{\mid }{V}_{cd}\mathrm{\mid }$ given by the global standard model fit, we obtain the $D^{+}$ decay constant $f_{D^{+}}=(213.5\pm {2.1}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {1.1}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}\pm {0.8}_{\mathrm{i}\mathrm{n}\mathrm{p}\mathrm{u}\mathrm{t}}\pm {0.7}_{\mathrm{E}\mathrm{M}})$,MeV. Alternatively, using the value of $f_{D^{+}}$ from a precise lattice quantum chromodynamics calculation, we extract $\mathrm{\mid }{V}_{cd}\mathrm{\mid }=0.2265\pm {0.0023}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.0011}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}\pm {0.0009}_{\mathrm{i}\mathrm{n}\mathrm{p}\mathrm{u}\mathrm{t}}\pm {0.0007}_{\mathrm{E}\mathrm{M}}$.