Measurement of the Pseudoscalar Decay Constant $f_{D_s}$ Using Charm-Tagged Events in $e^{+}{e}^{-}$ Collisions at $\sqrt{s}=10.58\mathrm{GeV}$

Using $230.2{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ annihilation data collected with the BABAR detector at and near the peak of the ${\rm Y}(4S)$ resonance, $489\pm 55$ events containing the pure leptonic decay $D_s^{+}\to {\mu }^{+}{\nu }_{\mu }$ have been isolated in charm-tagged events. The ratio of partial widths $\Gamma (D_s^{+}\to {\mu }^{+}{\nu }_{\mu })/\Gamma (D_s^{+}\to \varphi {\pi }^{+})$ is measured to be $0.143\pm 0.018\pm 0.006$ allowing a determination of the pseudoscalar decay constant $f_{D_s}=(283\pm 17\pm 7\pm 14)\mathrm{MeV}$. The errors are statistical, systematic, and from the $D_s^{+}\to \varphi {\pi }^{+}$ branching ratio, respectively.

Figure 1

Tag mass distribution, showing the signal and sideband regions, in events with a recoil muon. All tag modes are combined, scaling their mass and width to that of the $D^0\to K^{-}{\pi }^{+}$ mode.

Figure 2

$\Delta M$ distribution of charm-tagged events passing the signal selection. The tag can be from the tag signal region (solid lines) or the sidebands (dashed lines). In the bottom plot the signal muon is replaced with an electron to estimate the semileptonic charm and $\tau$ decay background.

Figure 3

$\Delta M$ distribution after the tag sidebands and the electron sample are subtracted. The solid line is the fitted signal and background distribution ($N_{\mathrm{Sig}}{f}_{\mathrm{Sig}}+N_{\mathrm{Bkgd}}{f}_{\mathrm{Bkgd}}$); the dashed line is the background distribution ($N_{\mathrm{Bkgd}}{f}_{\mathrm{Bkgd}}$) alone.

Figure 4

$\Delta M$ distribution of selected $D_s^{*+}\to \gamma D_s^{+}\to \gamma \varphi {\pi }^{+}$ events after the tag sideband is subtracted. The solid line is the fitted signal and background distribution ($N_{\varphi \pi }{f}_{\varphi \pi }+N_{\varphi \pi \mathrm{Bkgd}}{f}_{\varphi \pi \mathrm{Bkgd}}$; the dashed line is the background distribution ($N_{\varphi \pi \mathrm{Bkgd}}{f}_{\varphi \pi \mathrm{Bkgd}}$) alone.