First observation of the $B^{+}\to D_s^{+}{D}_s^{-}{K}^{+}$ decay

The $B^{+}\to D_s^{+}{D}_s^{-}{K}^{+}$ decay is observed for the first time using proton-proton collision data collected by the LHCb detector at center-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of $9{\mathrm{fb}}^{-1}$. Its branching fraction relative to that of the $B^{+}\to D^{+}{D}^{-}{K}^{+}$ decay is measured to be $\frac{\mathcal{B}(B^{+}\to D_s^{+}{D}_s^{-}{K}^{+})}{\mathcal{B}(B^{+}\to D^{+}{D}^{-}{K}^{+})}=0.525\pm 0.033\pm 0.027\pm 0.034,$ where the first uncertainty is statistical, the second systematic, and the third is due to the uncertainties on the branching fractions of the $D_s^{\pm }\to K^{\mp }{K}^{\pm }{\pi }^{\pm }$ and $D^{\pm }\to K^{\mp }{\pi }^{\pm }{\pi }^{\pm }$ decays. This measurement fills an experimental gap in the knowledge of the family of Cabibbo-favored $\overline{b}\to \overline{c}c\overline{s}$ transitions and opens the path for unique studies of spectroscopy in future.

Figure 1

Feynman diagrams contributing to the $B^{+}\to D_s^{+}{D}_s^{-}{K}^{+}$ decay.

Figure 2

Invariant-mass distributions of reconstructed (left) $D_s^{+}$ $D_s^{-}$ $K^{+}$ and (right) $D^{+}$ $D^{-}$ $K^{+}$ candidates. The fit results are overlaid.

Figure 3

Distributions of background-subtracted invariant mass of the (top) $D_s^{+}$ $D_s^{-}$, (bottom left) $D_s^{-}{K}^{+}$, and (bottom right) $D_s^{+}{K}^{+}$ systems of the $B^{+}\to D_s^{+}{D}_s^{-}{K}^{+}$ decay.

Figure 4

Efficiency as a function of the Dalitz-plot variables for the (top) $B^{+}\to D_s^{+}{D}_s^{-}{K}^{+}$ and (bottom) $B^{+}\to D^{+}{D}^{-}{K}^{+}$ decays, calculated separately for the (left) run 1 and (right) run 2 periods.