Precision measurement ofB(D+→μ+ν)and the pseudoscalar decay constantfD+

We measure the branching ratio of the purely leptonic decay of the $D^{+}$ meson with unprecedented precision as $\mathcal{B}(D^{+}\to {\mu }^{+}\nu )=(3.82\pm 0.32\pm 0.09)\times {10}^{-4}$, using $818{\mathrm{pb}}^{-1}$ of data taken on the $\psi (3770)$ resonance with the CLEO-c detector at the CESR collider. We use this determination to derive a value for the pseudoscalar decay constant $f_{D^{+}}$, combining with measurements of the $D^{+}$ lifetime and assuming $|V_{cd}|=|V_{us}|$. We find $f_{D^{+}}=(205.8\pm 8.5\pm 2.5)\mathrm{MeV}$. The decay rate asymmetry $\frac{\Gamma (D^{+}\to {\mu }^{+}\nu )-\Gamma (D^{-}\to {\mu }^{-}\overline{\nu })}{\Gamma (D^{+}\to {\mu }^{+}\nu )+\Gamma (D^{-}\to {\mu }^{-}\overline{\nu })}=0.08\pm 0.08$, consistent with no $CP$ violation. We also set 90% confidence level upper limits on $\mathcal{B}(D^{+}\to {\tau }^{+}\nu )<1.2\times {10}^{-3}$ and $\mathcal{B}(D^{+}\to e^{+}\nu )<8.8\times {10}^{-6}$.