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

Using $ 20.3\text{}\text{}{\mathrm{fb}}^{-1}$ of $ {e}^{+}{e}^{-}$ collision data collected at a center-of-mass energy of $ {E}_{\mathrm{c}\mathrm{.}\mathrm{m}\mathrm{.}}=3.773\text{}\text{}\mathrm{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 0.08{0}_{\mathrm{stat}}\pm 0.04{0}_{\mathrm{syst}})\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}^{+}}|{V}_{cd}|=(48.02\pm 0.4{8}_{\mathrm{stat}}\pm 0.2{4}_{\mathrm{syst}}\pm 0.1{2}_{\text{input}}\pm 0.1{5}_{\mathrm{EM}})\text{}\text{}\mathrm{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\to d$ Cabibbo-Kobayashi-Maskawa matrix element $ |{V}_{cd}|$ given by the global standard model fit, we obtain the $ {D}^{+}$ decay constant $ {f}_{{D}^{+}}=\phantom{\rule{0ex}{0ex}}(213.5\pm {2.1}_{\mathrm{stat}}\pm {1.1}_{\mathrm{syst}}\pm {0.8}_{\text{input}}\pm {0.7}_{\mathrm{EM}})\text{}\text{}\mathrm{MeV}$. Alternatively, using the value of $ {f}_{{D}^{+}}$ from a precise lattice quantum chromodynamics calculation, we extract $ |{V}_{cd}|=0.2265\pm 0.002{3}_{\mathrm{stat}}\pm 0.001{1}_{\mathrm{syst}}\pm \phantom{\rule{0ex}{0ex}}0.000{9}_{\text{input}}\pm 0.000{7}_{\mathrm{EM}}$.