Observation of $B_c^{+}\to D{h}^{+}{h}^{-}$ decays

Searches are presented for $B_c^{+}\to D{h}^{+}{h}^{-}$ decays, where $D$ is a charmed meson and $h^{\pm }$ is a charged pion or kaon, using $pp$ collision data collected by the LHCb experiment corresponding to an integrated luminosity of $9{\text{fb}}^{-1}$. The decays $B_c^{+}\to D^{+}{K}^{+}{\pi }^{-}$, $B_c^{+}\to D^{\ast +}{K}^{+}{\pi }^{-}$ and $B_c^{+}\to D_s^{+}{K}^{+}{K}^{-}$ are observed for the first time. Their branching fractions, expressed as ratios relative to that of the $B_c^{+}\to B_s^0{\pi }^{+}$ decay, are determined to be \begin{align*} $\mathcal{R}$(B_c^+\to D^+ K^+π^-) =(1.96 \pm 0.23\pm 0.08 \pm 0.10)\times 10^{-3},&\ $\mathcal{R}$(B_c^+\to D^{+} K^+π^-) =(3.67 \pm 0.55 \pm 0.24\pm 0.20)\times 10^{-3},&\ $\mathcal{R}$(B_c^+\to D_s^+ K^+ K^-) =(1.61 \pm 0.35\pm 0.13\pm 0.07)\times 10^{-3}, \end{align} where the first uncertainty is statistical, the second is systematic, and the third is due to the limited precision on the $D$-meson branching fractions. The decay channels proceed primarily through excited $K^0$ or $D^0$ resonances or $\phi$ mesons, and open a new avenue for studies of charge-parity violation in beauty mesons.