Measurement of the absolute branching fractions for $D_s^{-}\to {\ell }^{-}{\overline{\nu }}_{\ell }$ and extraction of the decay constant $f_{D_s}$

The absolute branching fractions for the decays $D_s^{-}\to {\ell }^{-}{\overline{\nu }}_{\ell }$ ($\ell =e$, $\mu$, or $\tau$) are measured using a data sample corresponding to an integrated luminosity of $521{\mathrm{fb}}^{-1}$ collected at center-of-mass energies near 10.58 GeV with the BABAR detector at the PEP-II $e^{+}{e}^{-}$ collider at SLAC. The number of $D_s^{-}$ mesons is determined by reconstructing the recoiling system $DKX\gamma$ in events of the type $e^{+}{e}^{-}\to DKX{D}_s^{*-}$, where $D_s^{*-}\to D_s^{-}\gamma$ and $X$ represents additional pions from fragmentation. The $D_s^{-}\to {\ell }^{-}{\nu }_{\ell }$ events are detected by full or partial reconstruction of the recoiling system $DKX\gamma \ell$. The branching fraction measurements are combined to determine the $D_s^{-}$ decay constant $f_{D_s}=(258.6\pm 6.4\pm 7.5)\mathrm{MeV}$, where the first uncertainty is statistical and the second is systematic.

Figure 1

$m_r(DKX\gamma )$ distributions for each $n_X^R$ value. The points are the data. The open histogram is from the fit described in the text. The solid histogram is the background component from the fit. The vertical lines define the region used in the ${\ell }^{-}{\overline{\nu }}_{\ell }$ selections.

Figure 2

$m_r(DKX\gamma )$ distribution for the total WS (left) and RS (right) samples.

Figure 3

Fitted distributions of (a) $m_r^2(DKX\gamma \mu )$, (b) $m_r^2(DKX\gamma e)$, (c) $E_{\mathrm{extra}}$ for $D_s^{-}\to {\tau }_{e\nu \nu }^{-}{\overline{\nu }}_{\tau }$, (d) $E_{\mathrm{extra}}$ for $D_s^{-}\to {\tau }_{\mu \nu \nu }^{-}{\overline{\nu }}_{\tau }$ candidates, and (e) $m(KK\pi \gamma )$. In each figure, the points represent the data with statistical error bars, the open histogram is from the fit described in the text, and the solid histogram is the background component from the fit.