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

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Abstract

We measure the branching ratio of the purely leptonic decay of the ${D}^{+}$ meson with unprecedented precision as $\mathcal{B}({D}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}\ensuremath{\nu})=(3.82\ifmmode\pm\else\textpm\fi{}0.32\ifmmode\pm\else\textpm\fi{}0.09)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, using $818\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$ of data taken on the $\ensuremath{\psi}(3770)$ 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 ${f}_{{D}^{+}}=(205.8\ifmmode\pm\else\textpm\fi{}8.5\ifmmode\pm\else\textpm\fi{}2.5)\text{ }\text{ }\mathrm{MeV}$. The decay rate asymmetry $\frac{\ensuremath{\Gamma}({D}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}\ensuremath{\nu})\ensuremath{-}\ensuremath{\Gamma}({D}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}\overline{\ensuremath{\nu}})}{\ensuremath{\Gamma}({D}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}\ensuremath{\nu})+\ensuremath{\Gamma}({D}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}\overline{\ensuremath{\nu}})}=0.08\ifmmode\pm\else\textpm\fi{}0.08$, consistent with no $CP$ violation. We also set 90% confidence level upper limits on $\mathcal{B}({D}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}\ensuremath{\nu})<1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and $\mathcal{B}({D}^{+}\ensuremath{\rightarrow}{e}^{+}\ensuremath{\nu})<8.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$.

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