Measurement of $B(D_s^{+}\to {\mu }^{+}{\nu }_{\mu })$

We present a measurement of the branching fraction $\mathcal{B}(D_s^{+}\to {\mu }^{+}{\nu }_{\mu })$ using a $548{\mathrm{fb}}^{-1}$ data sample collected by the Belle experiment at the KEKB $e^{+}{e}^{-}$ collider. The $D_s$ momentum is determined by reconstruction of the system recoiling against $DK\gamma X$ in events of the type $e^{+}{e}^{-}\to D_s^{*}DKX$, $D_s^{*}\to D_s\gamma$, where $X$ represents additional pions or photons from fragmentation. This full-reconstruction method provides high resolution in the neutrino momentum and thus good background separation, equivalent to that achieved by experiments at the tau-charm factories. We obtain the branching fraction $\mathcal{B}(D_s^{+}\to {\mu }^{+}{\nu }_{\mu })=[6.44\pm 0.76(\mathrm{stat})\pm 0.57(\mathrm{syst})]\times {10}^{-3}$, implying a $D_s$ decay constant of $f_{D_s}=[275\pm 16(\mathrm{stat})\pm 12(\mathrm{syst})]\mathrm{MeV}$.

Figure 1

Top: recoil mass spectrum for $D_s$-tags (for both RS and WS samples). Bottom: spectrum of missing mass squared for $D_s^{+}\to {\mu }^{+}{\nu }_{\mu }$ candidates for the selected data. Error bars represent the statistical errors. The dark-shaded areas show the fitted background; the light-shaded bands show the fit to signal and background with systematic uncertainties. The vertical lines indicate the signal regions.

Figure 2

Top: two-dimensional distribution in the recoil mass and $n_X^R$ for selected $D_s$-tags. Bottom: $\mathcal{B}(D_s\to \mu {\nu }_{\mu })$ as a function of $n_X^T$; the final result is shown as the dark-shaded region. For comparison, the 2006 world average value [11] and its error are shown as the light-shaded region in the background.