Precision measurements of $B(D^{+}\to \hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼)$, the pseudoscalar decay constant $f_{D^{+}}$, and the quark mixing matrix element $|V_{\mathrm{cd}}|$

Abstract

We report a measurement of the branching fraction $B(D^{+}\to \hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼)=[3.71\pm 0.19(\mathrm{stat})\pm 0.06(\mathrm{sys})]\times 10^{-4}$ based on 2.92 $\mathrm{f}{\mathrm{b}}^{-1}$ 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 $|V_{\mathrm{cd}}|$ 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 $|V_{\mathrm{cd}}|=0.2210\pm 0.0058\pm 0.0047$. In either case, these are the most precise results for these quantities to date.

6 pages, 2 figures