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

Abstract

Using $20.3~\mathrm{fb}^{-1}$ of $e^+e^-$ collision data collected at a center-of-mass energy of $E_{\rm c.m.}=3.773$ 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 $(4.034\pm0.080_{\rm stat}\pm0.040_{\rm syst})\times10^{-4}$. 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 $f_{D^+}|V_{cd}|=(48.02\pm0.48_{\rm stat}\pm0.24_{\rm syst}\pm0.12_{\rm input}\pm0.15_{\rm EM})~\mathrm{MeV}$ 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 $f_{D^+}=(213.5\pm2.1_{\rm stat}\pm1.1_{\rm syst}\pm0.8_{\rm input}\pm0.7_{\rm EM})$\,MeV. Alternatively, using the value of $f_{D^+}$ from a precise lattice quantum chromodynamics calculation, we extract $|V_{cd}|=0.2265\pm0.0023_{\rm stat}\pm0.0011_{\rm syst}\pm0.0009_{\rm input}\pm0.0007_{\rm EM}$.