Measurement of the Branching Fraction for $D_s^{+}\to {\tau }^{+}{\nu }_{\tau }$ and Extraction of the Decay Constant f_{D_s}

The branching fraction for the decay $D_s^{+}\to {\tau }^{+}{\nu }_{\tau }$, with ${\tau }^{+}\to e^{+}{\nu }_e{\bar{\nu }}_{\tau }$, is measured using a data sample corresponding to an integrated luminosity of 427 fb^{-1} collected at center of mass energies near 10.58 GeV with the \slshape B\kern-0.1em{\smaller A}\kern-0.1em B\kern-0.1em{\smaller A\kern-0.2em R} detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at SLAC. In the process $e^{+}e^{-}\to c\bar c\to D^{+}s \kern 0.2em\bar{\kern -0.2em D}{}{$\mathrm{T}\mathrm{A}\mathrm{G}$} \kern 0.2em\bar{\kern -0.2em K}{} X$,the$D^{+}_s$ meson is reconstructed as a missing particle, and the subsequent decay $D_s^{\ast +}\to D_s^{+}\gamma$ yields an inclusive $D_s^{+}$ data sample. Here ${}_{\mathrm{T}\mathrm{A}\mathrm{G}}$ refers to a fully reconstructed hadronic $\bar{D}$ decay, $\kern 0.2em\bar{\kern -0.2em K}{}$isa$K^-$or$\kern 0.2em\bar{\kern -0.2em K}{}^0$,and$X$standsforanynumberofchargedorneutralpions\mathrm{.}Thedecay$D^+s\to K^0{\scriptscriptstyle S} K^{+}$ is isolated also, and from ratio of event yields and known branching fractions, ${\cal B} (D^+s\to\tau^{+}\nu{\tau})$ = (4.5\pm0.5\pm0.4\pm0.3% is determined. The pseudoscalar decay constant is extracted to be $f_{D_s}$ = (233\pm13\pm10\pm7) MeV, where the first uncertainty is statistical, the second is systematic, and the third results from the uncertainties on the external measurements used as input to the calculation.