Measurement ofB(Ds+→l+ν)and the decay constantfDs+from600 pb−1ofe+e−annihilation data near 4170 MeV

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Abstract

We examine ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}_{s}^{\ensuremath{-}}{D}_{s}^{*+}$ and ${D}_{s}^{*\ensuremath{-}}{D}_{s}^{+}$ interactions at 4170 MeV using the CLEO-c detector in order to measure the decay constant ${f}_{{D}_{s}^{+}}$ with good precision. Previously our measurements were substantially higher than the most precise lattice based QCD calculation of $(241\ifmmode\pm\else\textpm\fi{}3)\text{ }\text{ }\mathrm{MeV}$. Here we use the ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\ell}}^{+}\ensuremath{\nu}$ channel, where the ${\ensuremath{\ell}}^{+}$ designates either a ${\ensuremath{\mu}}^{+}$ or a ${\ensuremath{\tau}}^{+}$, when the ${\ensuremath{\tau}}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}\overline{\ensuremath{\nu}}$. Analyzing both modes independently, we determine $\mathcal{B}({D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}\ensuremath{\nu})=(0.565\ifmmode\pm\else\textpm\fi{}0.045\ifmmode\pm\else\textpm\fi{}0.017)%$, and $\mathcal{B}({D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}\ensuremath{\nu})=(6.42\ifmmode\pm\else\textpm\fi{}0.81\ifmmode\pm\else\textpm\fi{}0.18)%$. We also analyze them simultaneously to find an effective value of ${\mathcal{B}}^{\mathrm{eff}}({D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}\ensuremath{\nu})=(0.591\ifmmode\pm\else\textpm\fi{}0.037\ifmmode\pm\else\textpm\fi{}0.018)%$ and ${f}_{{D}_{s}^{+}}=(263.3\ifmmode\pm\else\textpm\fi{}8.2\ifmmode\pm\else\textpm\fi{}3.9)\text{ }\text{ }\mathrm{MeV}$. Combining with the CLEO-c value determined independently using ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}\ensuremath{\nu}$, ${\ensuremath{\tau}}^{+}\ensuremath{\rightarrow}{e}^{+}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ decays, we extract ${f}_{{D}_{s}^{+}}=(259.5\ifmmode\pm\else\textpm\fi{}6.6\ifmmode\pm\else\textpm\fi{}3.1)\text{ }\text{ }\mathrm{MeV}$. Combining with our previous determination of $\mathcal{B}({D}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}\ensuremath{\nu})$, we extract the ratio ${f}_{{D}_{s}^{+}}/{f}_{{D}^{+}}=1.26\ifmmode\pm\else\textpm\fi{}0.06\ifmmode\pm\else\textpm\fi{}0.02$. No evidence is found for a $CP$ asymmetry between $\ensuremath{\Gamma}({D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}\ensuremath{\nu})$ and $\ensuremath{\Gamma}({D}_{s}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}\ensuremath{\nu})$; specifically the fractional difference in rates is measured to be $(4.8\ifmmode\pm\else\textpm\fi{}6.1)%$. Finally, we find $\mathcal{B}({D}_{s}^{+}\ensuremath{\rightarrow}{e}^{+}\ensuremath{\nu})<1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ at 90% confidence level.

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