Observation of $B_s^0\to D_s^{(*)+}{D}_s^{(*)-}$ Using $e^{+}{e}^{-}$ Collisions and a Determination of the $B_s\mathrm{\text{−}}{\overline{B}}_s$ Width Difference $\Delta {\Gamma }_s$

We have made the first observation of $B_s^0\to D_s^{(*)+}{D}_s^{(*)-}$ decays using $23.6{\mathrm{fb}}^{-1}$ of data recorded by the Belle experiment running on the ${\rm Y}(5S)$ resonance. The branching fractions are measured to be $\mathcal{B}(B_s^0\to D_s^{+}{D}_s^{-})=({1.03}_{-0.32-0.25}^{+0.39+0.26})\%$, $\mathcal{B}(B_s^0\to D_s^{*\pm }{D}_s^{\mp })=({2.75}_{-0.71}^{+0.83}\pm 0.69)\%$, and $\mathcal{B}(B_s^0\to D_s^{*+}{D}_s^{*-})=({3.08}_{-1.04-0.86}^{+1.22+0.85})\%$; the sum is $\mathcal{B}[B_s^0\to D_s^{(*)+}{D}_s^{(*)-}]=({6.85}_{-1.30-1.80}^{+1.53+1.79})\%$. Assuming $B_s^0\to D_s^{(*)+}{D}_s^{(*)-}$ saturates decays to $CP$-even final states, the branching fraction determines the ratio $\Delta {\Gamma }_s/\cos \phi$, where $\Delta {\Gamma }_s$ is the difference in widths between the two $B_s\mathrm{\text{−}}{\overline{B}}_s$ mass eigenstates, and $\phi$ is a $CP$-violating weak phase. Taking $CP$ violation to be negligibly small, we obtain $\Delta {\Gamma }_s/{\Gamma }_s={0.147}_{-0.030}^{+0.036}(\mathrm{stat}{)}_{-0.041}^{+0.042}(\mathrm{syst})$, where ${\Gamma }_s$ is the mean decay width.

Figure 1

$M_{\mathrm{bc}}$ vs $\Delta E$ scatter plots. The signal ellipses correspond to $3\sigma$ in resolution for ${\rm Y}(5S)\to B_s^{*}{\overline{B}}_s^{*}$ decays; the number of candidates within the ellipses is listed. The top, middle, and bottom plots correspond to $B_s^0\to D_s^{+}{D}_s^{-}$, $B_s^0\to D_s^{*\pm }{D}_s^{\mp }$, and $B_s^0\to D_s^{*+}{D}_s^{*-}$, respectively.

Figure 2

$M_{\mathrm{bc}}$ and $\Delta E$ projections of the fit result. The rows correspond to $B_s^0\to D_s^{+}{D}_s^{-}$ (top plots), $B_s^0\to D_s^{*\pm }{D}_s^{\mp }$ (middle plots), and $B_s^0\to D_s^{*+}{D}_s^{*-}$ (bottom plots). The (red) dashed (dotted) curves show RC (WC) signal, the (green and blue) dash-dotted curves show CF signal, the grey solid curve shows background, and the black solid curves show the total.