Precision measurements of $B(D^+ \rightarrow \mu^+ \nu_{\mu})$, the pseudoscalar decay constant $f_{D^+}$, and the quark mixing matrix element $|V_{\rm cd}|$

Understand

We report a measurement of the branching fraction $B(D^+ \rightarrow \mu^+ \nu_{\mu}) = [3.71 \pm 0.19 (\rm stat) \pm 0.06 (\rm sys)]\times 10^{-4}$ based on 2.92 ${\rm fb^{-1}}$ of data accumulated at $\sqrt{s}=3.773$ GeV with the BESIII detector at the BEPCII collider.

• This measurement, in conjunction with the Cabibbo-Kobayashi-Maskawa matrix element $|V_{\rm cd}|$ determined from a global Standard Model fit, implies a value for the weak decay constant $f_{D^+}=(203.2 \pm 5.3 \pm 1.8)$ MeV.
• Additionally, using this branching fraction measurement together with a Lattice QCD prediction for $f_{D^+}$, we find $|V_{\rm cd}|=0.2210\pm 0.0058 \pm 0.0047$.
• In either case, these are the most precise results for these quantities to date.