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

We report a measurement of the branching fraction $B(D^+ rightarrow mu^+ u_{mu}) = [3.71 pm 0.19 (rm stat) pm 0.06 (rm sys)]times 10^{-4}$ based on 2.92 ${rm fb^{-1}}$ of data accumulated at $sqrt{s}=3.773$ GeV with the BESIII detector at the BEPCIIcollider. 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 $|V_{rm cd}|=0.2210pm 0.0058 pm 0.0047$. In either case, these are the most precise results for these quantities to date.