Direct measurement of ${B(D}_s^{+}\to \phi X^{+})$

The absolute inclusive branching fraction of $D_s^{+}\to \phi X^{+}$ has been measured from data collected by the BES detector at a center-of-mass energy of 4.03 GeV, corresponding to an integrated luminosity of 22.3 pb${}^{-1}$. At this energy, direct pair production $e^{+}{e}^{-}\to D_s^{+}{D}_s^{-}$ has been observed. We have selected $D_s$ candidate events by reconstructing five hadronic decay modes $D_s^{+}\to \phi {\pi }^{+}$, $K^{0*}{K}^{+}$, $K^0{K}^{+}$, $f_0{\pi }^{+}$ and $K^0{K}^{-}{\pi }^{+}{\pi }^{+}$ and have searched for inclusive $\phi$’s in the recoiling $D_s^{-}$. We observed three recoiling $\phi$’s in the 166.4 $\pm$ 31.8 $D_s$ candidate events, which leads to the absolute branching fraction ${B(D}_s^{+}\to \phi X^{+}{)=(17.8\mathrm{}}_{-7.2}^{+15.1\mathrm{}}{}_{-6.3}^{+0.6\mathrm{}})\hspace{0.5em}\%$ and ${B(D}_s^{+}\to \phi {\pi }^{+}{)=(3.6\mathrm{}}_{-1.6}^{+3.1\mathrm{}}{}_{-1.3}^{+0.4\mathrm{}})\hspace{0.5em}\%$.